I don't want to use parsers

[Allyrion]

There are also instances in which having your own parser data could help to disprove others.

When I first hit endgame in the 2.0 days as a MNK playing on PS3, I was trying to get my Titan clear. I had looked at rotations and knew the basic fundamentals of my job but I'm not holding any illusions that I was anything above average. In any event, I get into a party for 6/8 or 7/8 from the same FC, who are trying to get a clear for one of their members. The BLM runs underneath Titan everytime he jumps and dies, as such we are fighting with 3/4 DPS the entire time while I didn't get hit by anything. After 3 wipes, they all suddenly drop and then say "MNK has too low DPS" and boot me. I wanted to quit trying at that point but saw another shout and joined that party, determined to try it once more. We ended up one shotting and I was told that my DPS was 'average'.

Basically I was average for a player just entering endgame but I didn't have high enough DPS to overcome the BLM constantly dying. Had I had any indication what my own DPS was from the game, I may not have felt as bad about the way the first party treated me.

Exactly.
Good parsers can show all that happened during a fight. All that parsers gives are facts and numbers.
What players do with them is up to the players themselves. The players that would abuse them, probably already are anyway. They're just not saying it.

Information is a good thing, and with good parsing things beyond 'who has the highest dps' can be accounted for.
There's nothing wrong with knowing where you stand. Unlike healing or tanking, dps has a more fluid effect.
It's great if the content got cleared, but you should know if you got carried.

Progression isn't only about getting gear, it's about learning the fights too. It's about improving as a player as well.
I know some people get antsy at the thought of competition, but it's not even about that.
Any notion of progression in an MMO otherwise should involve trying to be better.
Otherwise you'd wipe once on a boss and drop the game forever.

That's not the case. People try to figure out their mechanical mistakes. It's reasonable to expect them to figure out how to maximize their job as well.
Parsers provide the information to allow for that.
People are jerks no matter what. Why should such useful information be held back so some could be blissfully ignorant?