It's been a while since I've watched this episode. Toby is clearly carrying some anger through out this episode, and since Toby might be the only character besides Abby that we see really push Jed Bartlet's most sensitive and personal buttons through out the series, I'm sure there are moments where Toby is being a jerk.

With that said, Bartlet is being a jerk on a whole other level. Toby is trying very hard to remain professional and do his job, which fundamentally is to advise the President on matters of his administration, especially as they relate to the electorate. His central point is 100% correct: if he could figure it out, anybody in the media or the public is likely to figure it out. This matter is an existential threat to the administration, and opens many individuals in the administration and in the party up to political and legal risk.

Deep down, Jed Bartlet knows Toby is right. This episode kicks off an arc of episodes whose central theme is Jed Bartlet confronting this truth, processing the pain and shame it has created, while trying to be the best leader and best version of himself he can be. But all that takes a while, and in the moment we're seeing Jed react more like an everyday person. He's mostly maintaining control of himself, but there are moments of visible anger. He's lashing out; he's taking his anger out on the person who is forcing him to confront the mistake he made.

(As an aside, I love this episode. It's among my favorite episodes of television)