Well, excuse me, who are you to judge?!

Said the kettle to the pot, when calling it black.
And this is a very tricky question indeed.
Because nobody is perfect. No one.

But does one have to be flawless to be able to observe?
I think not.

If you are offended by someone, then ask yourself why. Obviously, they hit a weak spot. And you can always reason your way out of every situation. But what does that really do in the end - nothing.

Rather by analyzing the facts and weighing out your part in it - how ever little you feel it may be; it does not matter, what matters is that you take ownership for your part - you are able to perfect your skills and improve.
Regardless of how black and dirty the person who called you out may be.

That person may be an excellent observer still, because you are mirroring their own imperfections; and isn't it always so obvious to pick up our own insecurities and personal struggles in others, because we know them oh-so-well? So, yes, we have every right to react with anger when called out for our flaws but does that make YOU a better person at the end of the day?
No, that just makes you stay in your shell and be a dirty, black pot instead of scrubbing yourself clean.

The choice is yours - you can't change others, but you can change yourself.
You just have to decide to do it: Choosing action over the all-to-tempting reaction pattern that is so hard-wired in our brains, but only serves as a one-way road to a negativistic outcome in life.