Give her your phone number if you want to leave it up to her to decide whether or not to contact you. Personally, I think the guy should go with the second alternative. Neither is superior. If you ask for her phone number, you will typically get the results sooner. If she doesn't call you within a few days, then she didn't find you attractive enough to give you her number.
However, if you don't ask for her number, you may never know if she wanted to meet up with you or not. So, it's up to you how you want to play it but either way, you'll be missing out on some interesting opportunities.
While talking to a female, just tell her you need her phone number so the two of you can meet up. Of course she'll want to give it to you, since she's just as interested in you as you are in her. But first, make sure it's okay with her parent(s) before you ask for their daughter's number.
If she doesn't give you her number right away, that's normal. She may want to think about it for a while and then call you back. If she doesn't, that's also normal. You two will probably have more success if you don't keep contacting her looking for her number.
The only exception to this rule is if you're both students at the same school. Then you definitely want to get her phone number so you can text each other later. Without texting, you'd never be able to stay in touch with each other outside of class.
Students usually like knowing they're being asked out. If she says no, there's no harm in asking again with a new approach. Maybe change the wording from "phone number" to "message me back." That way she knows you're not trying to take advantage of her kind nature.
Of course, you shouldn't take "no" for an answer.
It depends on the female and the cultural environment, but if she is interested, she should give out her phone number and allow the guy decide whether or not to call her. Absolutely. And it is generally the only indication that they are seriously interested in you. Don't, however, text her. That's just creepy.
Giving your number out too soon can be dangerous. If you do so before you know someone well, they could take advantage of you. It's best to be safe than sorry. But if you want to put your mind at ease, then feel free to give them out sooner rather than later.
You must provide a woman your phone number. When you ask for hers, she is forced to respond "yes" or "no," and she may not want to hurt your feelings. Yes, you run the chance of her not calling if you give her your phone number. However, there are ways around this problem.
If you give a woman your phone number, she should call you within 24 hours. If she doesn't, then you shouldn't worry about it. She might be busy or have other plans.
If you do get a call from a stranger asking for your number, just ignore them. They might be a scammer trying to steal your identity. There have been cases where people have given out their numbers without knowing what happened to them later on. One example is an individual who gave out his number while working at a bar. He never heard back from any women but suspects that maybe one of them sold his information to a scammer.
In conclusion, giving a woman your number is a good idea since it shows that you are interested in her. Make sure that you give her enough time to call you though as sometimes things happen that we aren't aware of. If you don't get a call within 24 hours, then don't worry about it.