The third man argument says that for every form that resides over some group of things, there will have to be another form that can account for that group and the form. Necessitating an infinitude of any individual form.
But the reason I could never understand it is this: doesn't the form already account for itself? That is, the form is what is common to the group of particulars and itself, and there doesn't need to be another form to account for their commonality.
For example, if I made a factory that creates plush toys that resemble me, we would say that I constitute the character common to them. But I also constitute that character by being myself. So to the question of "what constitutes the character common to me an my plushies?" Isn't the answer simply "me"?
Why can't this same logic apply to forms?