Seeing as it is the equivalence that is the bone of contention, claiming false equivalence seems to beg the question: it rests on your assumption that your position is the right one.
I'll add that in your initial equivalence you used the word 'try' in one case, but not the other. I.e., the monster attacks me, but he tries to intimidate me. Which is telling, but you could also correct that and make your same point.
I'll actually break with
@Charlaquin here, with whom I usually agree, and and say that I don't think it's a false equivalence. However, there is still a difference between the two: the game contains specific rules for the mechanical consequences of a successful attack (e.g. hit point loss, etc.), but there is:
a) No such thing as an "Intimidation action" (unlike, say, a Shove action, or a Hide action). The only rule that interacts with the Intimidation skill is the player action declaration -> DM adjudication loop.
b) No specific mechanical consequences are tied to a successful attribute roll using Charisma (Intimidation)
That is, a successful attack roll leads to the player "being hit", which they cannot unilaterally declare as not happening, which in turn causes hit point loss.
What does a successful "Intimidate" do? Results in the player being "Intimidated?" Sure, you could say that the player doesn't control whether or not the monster tried to intimidate them or attack them, and whether or not they successfully hit or intimidated them. But what does the latter mean? What mechanical implications does that carry? Are there further action declarations they may or may not make?
So therefore it's not "false" equivalence as much as...moot. There is no point to having a monster "roll Intimidation" unless you want to:
a) Use it as a roleplaying cue
b) Implement a house rule