Generic laptop vs self built desktop?

What are the pros and cons of each? And are desktops really being phased out like I keep getting told? I want to build a gaming desktop and can get all the parts I need for around 1.5k, which would cost over 3.5k in a custom laptop, and my parents want me to get a generic laptop which can just run Microsoft and Internet, because desktops are phasing out and people are going smaller(which isn't true, iPad is younger than itouch, iphone 5 is bigger than others). But if I can see the pros and cons of each, then I can see if I really should just get a laptop, or if self built desktops are way way way better, then maybe I can convince them to let me build it.
So basically, pros and cons of self buit desktop vs higher end generic laptop. And are desktops really phasing out?

If youre about to go to college, or you're a junior ore senior in high-school now, you're gonna need a laptop for college. Trust me, there's very little time to play serious gaming in college.

Just go desktop, bigger screen much more combinations with multiple screens better graphics (1.5k custom desktop most likely has SLI which laptops can't do)