What does anava lo lishma mean?
Tosfos says it means out of gaava. What does that mean? The chok nasan explains by limiting the whole issue to a personal tochacha -- when a person does something bad to you and need to give tochacha back to the person, i.e. that you are personally involved. This matches perfectly with the story later on with Rav Huna and Rav Chiya bar Rav. The anava is then easily understood that he says he should not give tochacha for his kavod. But its lo lishma since your real motivation is not to cause him anger. (seems to work perfectly in language of tosfos)
The gemara does not limit the tochacha explicitly which is why Rashi does not learn like this and understands that a person claims to be an anav, most likely building on the earlier gemara -- i am not qualified to give tochacha since he will say to me "טול קורה מבין עיניך" but the real motivation is to not get on his bad side.
Maharsha says the question is -- is it preferable to give tochacha even if it leads to embarassment or hold back to prevent embarassment and to this the story later on answers -- better to hold back and not embarass. This works well with the conclusion of the earlier gemara that no one today can give tochacha properly.