You may be the greatest player (I am not), you may be the life of the party, but the people who went to the trouble of starting a group have every right to invite whoever they want. That's how the tool works. Why should you care, let alone be offended, if who they choose isn't you?
If you run that content often, you probably have the credentials/code word/secret handshake they are asking for to join. If you don't and are a stranger, why be surprised they chose someone else?
If you are really that good, surely someone has noticed. You should have friends and/or guild mates you can group with for group content.
If you have no friends (in game friends, not talking about RL here) or guild mates willing to run with you, and have no credentials to prove your experience, why in the world would you feel entitled to join a group of strangers who don't know you from Adam?
I mostly run with friends and guild mates, but occasionally pug on one of my alts. I apply to some groups and get rejected plenty, but I don't stress over it and sure don't take it personally. Those people don't know me and their rejection isn't about me; it's about what they are looking for and what was in queue and which applicant first caught their attention as meeting their needs. Either way it's their group and they have every right to invite whoever they like.
Who cares if they are asking for Cutting Edge while the WF race is still going? Who cares if they want M+ score that is impossible to achieve? Who cares if they only want players with purple transmogs? That's the beauty of Group Finder; people can start any crazy group they want and invite whoever strikes their fancy. You don't have to apply if you don't like what they are up to.
I just don't get how people can be like "No I'm not in a guild. No I don't have friends. No I haven't already killed those bosses. No I haven't bothered to build a good M+ score. But damnit those people should have invited me and it's BS that they didn't!"
Plenty of groups doing easier content who are less picky. Build your friends list - players who've seen you in action and know what you can do - build those credentials and eventually more invites will come.