Sorry if I touched a nerve. If you'd like to quote what I wrote that you consider are gaslighting and mindgames I'd like to know.
As for what I was responding to:
You wrote, "No, it was made abundantly clear in the episode. From the beginning of the episode with the Batel breakfast scene, Pike doubts that Romulans are a threat"
Pike questioned how the Romulans can be blamed when no one knows what a Romulan looks like. That does not mean he doubts they are a threat.
BATEL: Keep hearing rumors the Romulans are developing new weapons.
PIKE: Ah, the Romulans are the bogeymen. No one's ever seen one. Nobody even knows what they look like, and yet they get blamed for a lot of things around here.
BATEL: Some actually there fault.
You wrote, "Later it's made clear that Pike hesitates too long". Watching the episode you would see that when Kirk requests Pike to fire on the Romulan that the Enterprise is
out of range and Pike tells Kirk that. Kirk says to fire anyway to draw their fire and Pike issues the order to fire 5 seconds later while still out of range. Contrast this to Kirk's 16 second delay before ordering weapons to be fired during the comet battle. There is no support that Pike hesitated when the Enterprise was out of range.
KIRK: Something isn't right.
SPOCK: The captain is correct. We should be seeing them by now.
KIRK: Enterprise, I don't like this.
SPOCK: Reading gravitational signature again. It's behind the Farragut.
PIKE: Kirk! Get out of there! Red Alert!
KIRK: Red Alert!
PIKE: Erica close that distance as fast as you can.
KIRK: Attack pattern Tiberius 4.
KIRK: Get behind them. (The Farragut loop instead steers head first into the Romulan.)
KIRK: Fire! (Kirk issues fire order 16 seconds after ordering "Attack pattern Tiberius 4")
(Romulan maintains fire, charges plasma bolt and hits Farragut with it).
KIRK: Fire phasers, Captain.
PIKE: We're out of range. We're just as likely to hit you as them.
KIRK: Maybe you'll draw their fire.
PIKE: MItchell, full phasers, now. (Pike issues orders 5 seconds after Kirk says "Fire phasers, Captain")
MITCHELL: Holy... We actually clipped them. (Enterprise fires phasers 7 seconds after Kirk says "Fire phasers, Captain")
PIKE: Nice shooting, Jenna.
You wrote, "and he doesn't want to destroy them." This part is correct. Pike wanted to neutralize the Romulan.
PIKE: Captain's personal log, stardate 1709.2. Per Captain Kirk's plan, we are mounting a pincer move. Our two ships will slowly drift closer as the Romulans remain unaware. When they pass through the comet's tail giving us their exact location, we will be in weapons range. Kirk, however, has agreed to my plan to neutralize, not destroy, the Bird-of-Prey, leaving open the possibility of dialogue.
You wrote, "It's Kirk who says that something is wrong after the comet." And it was also Pike yelled to Kirk to get the "Farragut out of there". See dialogue above.
You wrote, "Later Pike trusts the Romulans during the two-hour break" You leave out why Pike even need a two-hour cease-fire. He needs it because he's getting time for the Enterprise's repair crews to fix the weapons damaged while rescuing the Farragut. The cease-fire also stopped the Romulan's motion towards Romulan space.
SPOCK: Before they cloaked, I was able to scan the Bird-of-Prey. They are trailing trilithium fragments. Their power supply is damaged. I do not believe they have enough to make it back to Romulus.
KIRK: Do we know their position?
SPOCK: Yes. On a heading for the Neutral Zone. We could overtake them.
PIKE: What is the status of our weapons?
SPOCK: Our offensive capabilities are limited. Phasers are down. And torpedo launcher tubes sustained damage in the attack.
KIRK: But the Romulans don't know that.
PIKE: They will if we pull up on their six and can't fire. Lieutenant Uhura, open a channel to the Romulan ship.
UHURA: Sir? They haven't responded to any of our hails before.
PIKE: I know. Open a channel. We're going to send them a message.
...
ROMULAN COMMANDER: Our peoples are indeed different, Captain. In our culture, your words are a show of weakness. What chance does dialogue offer, save to delay me? Why should I listen to you?
PIKE: Both our ships are damaged. Your cloak is unstable, which leaves you vulnerable to our weapons. Maybe you have enough power to attack us. Maybe you have enough power to get back to Romulus without repairs. Conversely, maybe we can marshal our weapons and destroy you before you make it to the Neutral Zone. Or perhaps we chase you across the border and destroy you and get out before anyone's the wiser.
ROMULAN COMMANDER: So what is it that you're suggesting, Captain?
PIKE: A good faith gesture. Two hours. Enough time to repair our ships and bury the dead. And maybe this bit of mercy will lead to something further and better between our two cultures.
ROMULAN COMMANDER: Two hours.
...
SPOCK: Sensor readings suggest the Romulans have stopped forward movement.
You wrote, "and doesn't devise a backup plan. It's Kirk who comes up with one." What backup plans are available to Pike that he wouldn't have reasonably explored? There are no Star Fleet ships that could reach them in two hours. The only option Pike had if something went wrong is to warp away in retreat. Points for Kirk who comes up with a bluff and that is why Pike takes a liking to Kirk.
KIRK: I'd like to explore a backup plan. If you'll give me the resources.
PIKE: I'm listening.
KIRK: Look the Romulans just bought themselves some time. Sure, they can use that time to make repairs. But remember, they're on the edge of the Neutral Zone. They could also use it to call for reinforcements. So, what if we did the same? Just in case they decide to turn and fight after all.
PIKE: Jim, we're on the far edge of Federation space. It takes days to get a message to Starfleet. We're weeks away from help getting to us, even at maximum warp.
KIRK: But the Romulans don't know that.
PIKE: Captain Kirk... what are you suggesting?
KIRK: Captain Pike... can I borrow a shuttle?
You wrote, "Finally, the writer's use Kirk to explicitly state the problem by wondering what would happen if they had just blown the BoP out of the sky."
Yet despite all of Kirk's venting it was he who screwed up the one opportunity to get the Romulan during the comet battle. With the Farragut destroyed and the Enterprise weapon-less what other opportunities did they have during the episode to destroy the Romulan?
You wrote, "That was the correct course of action, but Pike didn't want to do that. He wanted to go gentle on them, hesitated, and then didn't come up with a backup plan."
Pike fired full phasers on the Romulan, despite being out of range while saving Kirk who rushed in and got shot in the face by a plasma bolt. The Enterprise lost her weapons while saving Kirk and Pike convinces the Romulan to stop running for two hours in an attempt to get Enterprise's weapons repaired and find a diplomatic solution to the problem. What reasonable backup plan did Pike have available to him? Kirk came up with an unusual backup plan to bluff the Romulans in case they called for reinforcements knowing that there are no Starfleet reinforcements close by.
You wrote, "In short, Pike just didn't take the Romulans as a serious threat. And that was made clear multiple times and in multiple ways throughout the episode."
Given that Pike requested for and accepted the help of the Farragut when he didn't have to would suggest Pike took whoever attacked Outpost 4 as a serious threat. Also, if Pike didn't consider the Romulans a serious threat why does he yell for Kirk to escape their trap? Surely if they weren't that dangerous he would've told Kirk to take them head-on, right?