The sentence that lets you get away with almost any annoying behavior ...
Actually, staying true to yourself and being who you are is not bad advice. If we didn't do that, we would all blend together into some average boring person.
But sometimes, the "need to be me" gets in the way of becoming a better version of yourself and building great relationships with others.
Here's an example where my own "need to be me" is being counterproductive:
My parents-in-law and brother-in-law are very close to us and constantly want to stay in touch and be updated about everything that's going on in our and their lives. We have a Whatsapp group for that purpose which has over 100 messages per day flying around. Now, I have heard of some complaints that I'm not active enough in this group. My first reaction: This is just not me! I'm not into sharing every single thing that I'm doing or commenting on other's every step. I keep my focus sharp on my work for most of the day and don't react to messages which are mostly trivial and not important.
I have two options now: I can stick to "being me" and possibly alienate my family. Or I can get over myself and make an effort. I'm trying the latter right now. Let's see how long I can keep this up before I naturally gravitate towards my previous behavior (probably until I'm reminded again).