A question

Is it considered unremarkable and acceptable behaviour to ask for a stranger's contact details (namely, a phone number) immediately upon engaging with them online? And is it considered unremarkable and acceptable behaviour to give it upon such a request? And is it therefore considered bizarre, rude, anti-social or verging on the hysterical to refuse?

I am completely baffled by this. Common sense tells me that asking for a stranger's number is presumptous and riven with the potential to go wrong, but when I tell them no, they act like I'm being unreasonable or that I just need to be persuaded.