One thing nobody here really seems to consider that Brink is featuring off-hand grenades. This is very different from the ‘grenades as weapon’ implementation in Wolf(ET)/Doom 3/ETQW/Half-Life/etc.
Grenade systems:
Wolf(ET): switch to the weapon using the dedicated button (which takes N time) or use the mouse wheel to scroll to it. Now you hold down the fire button to prime it, release to throw
Doom 3: dedicated grenade button. Press it once, it toggles to grenade. Press it once again, it returns to whatever previous weapon you had selected. Firing the grenade works similar to Wolf(ET), hold fire to prime and release to throw.
ETQW: essentially the same as Wolf(ET) iirc
Brink however has off-hand grenades. Now way back in TF/Q3F/TFC or whatever variant you played tended to have these as well. For TF everyone just scripted their own behaviour. For Q3F we exposed two of the most popular ways of throwing. One of them is the one that is in Brink now, a dedicated button for a grenade, you press it for priming, release for throwing. The more hardcore players tended to use the other system - which does require a bit more attention and isn’t as friendly to new players. Namely, you press the dedicated grenade button once to prime it (your grenade timer audio starts ticking) and you press it once more to throw it. The Team Fortress games were much more a twitch based shooter than the current generation of games tend to be, so hardcore players tended to go for the latter option as it required the least attention and provided the fastest way to throw a grenade (no weapon switch delay, no movement restrictions, etc). However, as I said, this isn’t as new player friendly as it is easy to forget about your primed grenade which then blows up in your face, taking you out with it.

I hope BRINKpro can do something about it 