My head canon has always been that Sisko is deliberately coming down hard on him there, to get to the bottom of it, to see what Nog's motivations truly are and to weed out any bullshitting.
I don't think you even need head canon for that. IMO, that's clearly what is going on and intended to be read that way.
Edit: The script explicitly states it:
NOG
(finally blurts out the truth)
Because I don't want to end up like my father.
Sisko calms down. He was only acting angry to push Nog to reveal his reasons for wanting to join Starfleet.
-----
There's also a great omitted scene in the script for the episode, taking place after Sisko and Dax discuss Nog's motivations:
SISKO
Okay, so we know he's a hard worker,
but the question remains: Why does
he want to join Starfleet?
DAX
I have no idea.
SISKO
So we still can't be sure if he's
serious or if this is all part of
some elaborate scam.
Before Dax can answer...
Quark and Rom approach Sisko.
QUARK
Commander, we need to talk.
SISKO
Go right ahead.
QUARK
It's about my nephew.
SISKO
Somehow, I'm not surprised.
QUARK
Rom, tell Commander Sisko what's on
your mind.
ROM
Well, the thing is... I'm not quite
sure...
QUARK
(interrupting)
What my brother's trying to say is
he's furious that you'd even consider
allowing his son to attend Starfleet
Academy.
(to Rom)
Isn't that right?
ROM
Well, I...
QUARK
(interrupting)
You see. He can barely speak he's
so angry. Now we... I mean, he...
demands you refuse the boy's request
and return his latinum immediately.
SISKO
Rom, is that what you want?
ROM
The thing is... we've always
assumed... that is... I did promise
that Nog would become... my brother's
apprentice...
DAX
That explains things.
QUARK
Lieutenant, please, this is between
my brother and Commander Sisko.
SISKO
Actually, that's not true. Your...
brother's feelings aren't at issue
here. According to both Federation
law and Ferengi tradition, Nog is
old enough to make his own decisions.
ROM
You see, brother, I told you.
SISKO
(to Quark)
And as for the latinum, must I remind
you of the first Rule of Acquisition?
ROM
(smiling)
"Once you have their money, you never
give it back." It's one of my
brother's favorites.
(to Quark)
Isn't that so, Brother?
QUARK
I'm not going to stand here and argue
Rules of Acquisition with a human.
DAX
Especially one who knows them as
well as you.
QUARK
(ignoring her, to Sisko)
That apprenticeship money is
rightfully mine. And I will protest
your actions to the Nagus himself if
I have to.
SISKO
Give the Nagus my best.
ROM
Can we leave now, brother?
The two of them start to walk away.
QUARK
Would you stop calling me that?
ROM
Calling you what?
QUARK
"Brother."
ROM
But you are my brother.
(a beat)
Unless mother lied to us.
QUARK
(wistful)
If only that were true.
As Rom and Quark walk away down the Promenade...
45 CLOSE ON SISKO AND DAX
As they exchange an amused look.
DAX
So I take it you are going to write
Nog's letter of recommendation?
SISKO
I don't know. That depends on Nog.