Some context. She wasn't honest about her reason for being there. The whole encounter, set up by her, is a bait & switch, to get on board as a guest, by manipulating command & Picard, implying she's impressed with his work, but really is there to judge it, make him uncomfortable about it, & has clear animosity for him over it. Anyone else would've spun her around & put her back on the transporter pad immediately, rather than be surprisingly subjected to that. The End. Roll credits. No one has time to be justifying & defending themselves to a designer, with no authority over them. I seriously would've asked her if she was joking about "mucking up her engines" & if not, to GTFO, cuz IDGAF.
But he likes & respects her, and wants to be liked an respected by her, maybe at least have her as an ongoing collaborative resource, which was the whole point of the hologram to begin with. He needed a live engineer to collab with, not the computer, the actual human designer, who knows the engine intimately enough to improvise with it. Having that personality IS the collaboration. It's a wonder they don't already have such a designer collab in the files, like her as an EMH for the engines, that they'd have set, so no other, "too personal", interactions get tripped into, by oddballs like Geordi, who use the whimsically clueless computer to accidentally program sentient holograms, as a hobby.
So, he doesn't send her away, like I would. Furthermore, at this point, him being openly honest about the full nature & history of him liking and wanting to be liked by her (which he still should've) only serves now to make things worse, because she clearly already doesn't, & will be repulsed by it, regardless of how innocent it was. (& it was) That's not an excuse for him to be dishonest, but her misrepresenting herself does exacerbate his situation, & him choosing to be dishonest, in the face of it, just to be liked, has a little understandable context, that I can extend a modicum of empathy to, given he's otherwise a decent person.
So he isn't openly honest, and that's wrong & inexcusable, but I can understand, & slightly empathize, because now he's on the defensive & trying to be liked, which is historically his weakest personality trait. He fumbles the hell out of it, by trying to manipulate how he's going to be perceived.
He isn't outright fabricating blatant lies. He's withholding, & coloring the circumstances. He's running spin & damage control... Badly, & he shouldn't be, and in the end, he admits he should've told her the whole truth, and yes, it was after she apologized for coming there with her own prejudices, which she did. (Should it have been presented in the writing as badly as that? No, but this is 35 year old soap opera. Times were different)
Ultimately, she came there to make him uncomfortable with prejudice & dismissiveness. He resultantly & disingenuously fumbles & made her uncomfortable, with inappropriate ingratiatory behavior. He began with the wrong impression. She's got some wrong impressions of her own, (I maintain her impression about the hologram was wrong) which is why he reacts badly & was at fault for that behavior. Yes, the episode does a period specific bad job of representing that, but they do find a way forward, and it's not entirely unrealistic that they would, after a real collaboration, and having some forgiveness & empathy within them, which I'm apt to also have within myself.