Women's are like to admire

we like appreciation and sincerity more...

That's not entirely true, women like to be admired by the right person but when anyone else does it they feel offended or insulted. To be fair though it's not just women that are like that most men are the same way.

Most people like to be admired.
Do you know anyone that has ever said "I'm tired of all this admiration! I just wish people wouldn't admire me. I am going to start doing things to make sure people do the opposite of admire me just so they won't admire me."

Other than that, could be for lots of reasons.

Anywhere from:
- Women mate by choosing an individual male from a plethora of suitors.
How a man communicates "admiration" offers information about him, how he sees her, and helps her make her choice.

- Traditionally speaking women were seen as "lesser" or "fairer" to men.
Admiration offers social validation.
You ever see any 80's film where the "nerd" tries out for football, or the popular crowd, saves the day, and then everybody likes them, sees them as a unique special snowflake individual?
Same principle.

- People are constantly vying for a higher social position.
Higher social position means greater social security.
Similar to the principle of "I don't have to run faster than the bear, I just have to run faster than you."
Admiration bestows a level of worth, pushes you ahead of others.
People get shot, killed, beat up, mugged everyday.
Presidents don't.
Greater protection by others to keep them around because they're seen as "worth" more.

- It means you've accomplished something. People feel better with a purpose and fulfilling/completing something.
Admiration can be an extension of that, acknowledgement of doing something.

- Validation of shallow vanity.

To:
- It just feels good and they don't overthink it.

Lots of reasons.

Unless:

there's a language issue?
Like instead of "admire" you meant "fawned over," or, "told what they want to hear," or, "ego stroked," or something like that?

Because the obvious is not always obvious