In light of the controversies surrounding moguls like Harvey Weinstein and Steve Wynn as well as stars like Kevin Spacey, Aziz Ansari, and several other names, it is unsurprising that men are uncomfortable. Everything they have ever been taught by society about how to treat a woman is being turned upside-down (by the same women that they're trying to compliment.... just take the compliment).
Well, sir, this is for you. First, I would like to say that it is not entirely your fault. You were raised in a society by people who did not teach you the difference between "you look nice today" and "Great ass, sweetheart!". This same society that teaches boys and girls alike that money and stardom gives you power, and therefore "you can do anything" (apparently including grab a woman's vagina).
For you, I'd like to give some advice, NOT CRITICISM, advice.
Yes, women do like to be complimented, you're right about that; all humans like compliments and all humans like respect. So, generally, If you wouldn't say it to your boss or your grandmother, don't say it to a girl on the streets.
Example: "your tits look bomb af in that top" is not how you greet grandma at Thanksgiving or ANYWHERE for that matter. Therefore, don't yell it at some random chick on 5th Avenue.
Your next lesson is that no means no. Trust me on this, because if your girl is "playing cute" by saying no, she doesn't need you. This is a boundary that us women need to work on too by making our motives and mindsets clear.
We really do need to stop playing coy and saying "no" to appear virtuous when we really mean yes, because it creates a scary gray area to sexual assault that should not exist. Therefore guys, even if she's playing, just respect that no. If she reacts and says yes without pressure, then you're free, but don't take the risk.
Finally: Stop taking things so personally. Just because women don't want to get yelled at doesn't mean that they don't want to be spoken to.
A hug is acceptable as long you don't grab her butt. Asking where the stapler is will not get you a sexual harassment report unless you have your penis out. So stop blowing things out of proportion (which, interestingly is a trait that many men say women have naturally).
I hope this helps,
A Human with Common Sense