i'm confused right now. since last friday i finally got my GTX 960 thanks to my dad. however, i forgot how long it has been, but i also have an AMD processor (AMD A8-6600k), and it's pretty loving old. before i got the GTX 960, i had an AMD Radeon 7770 -which is 3 years old- of course, i had no crashing problems or anything like that except i couldn't run games smoothly. i've had a bsod while having my gtx 960 but it was because the heat sink attached to my amd processor was dusty.
the main issue though is that i've done a lot of research on a comparison between intel cpus and amd cpus, and what happens if an amd cpu and an nvidia gpu mix together after i've been told by a friend that my computer will forget up if i add the two together. so far since 5 days i barely had any problems with it after testing a few big games with it: far cry 3 runs smoothly, rainbow six siege gives me a few freezing points and frame rate drops at the start but after playing on the same map it seems smooth also. but i've heard that i'm basically 'bottlenecking' my computer and i should replace my AMD processor to an intel if i can.
dad has been a bit irritated about me mentioning a new processor in front of him and keeps asking me why i need one if it's necessary, because he looked at me playing a game smoothly and he thought it was alright. however, dad has been thinking about getting a new processor for me, but not today or tomorrow (which im not complaining). if his reason was because of a money issue, i would understand and i would be patient about it. but he's making a completely different reason as to why i should have a new processor if i'm running games ok.
here is my rig in case if you people ask for it:

i don't know what to do honestly, do i just keep up with the current rig i have right now or do i upgrade a new processor before bad things happen? i'm probably overthinking about it and i'm worried about it also. if i do need to upgrade though maybe i should just make my own money instead of talking to dad about it.