My girlfriend doesn't like it when I discipline our children

Basically our oldest child is 3 and lately he will scream and stomp whenever he doesn't get his own way. My approach is to say no and not let him get his own way and I would let him kick and scream until he gets it out of his system and then explain why I said no. However my girlfriend just wants to give him what he wants a d if I try and do it my way she will eventually undermine me and even get angry with me saying it's easier to just let him have what he wants so he stops playing up and also she cites his age, saying he's only so why am I being so cruel.

Personally I think my approach will set him up for a better future where my son can control his feelings when things don't go his way and he doesn't get his own way but am I right, am I being too harsh?