I blame the way you've tried to explain it rather than confusion on my end.
If you tell me that our environment and genes 100% decides my choices in life, then that is fate.
No, it isn't. Fate means that the future is already set. Determinism and fatalism are not the same thing. Fatalism suggests that the future is set, but does not necessarily say anything about free will. In other words, you could be a fatalist who believes entirely in free will, but you would be unable to avoid getting married to Julia in 10 years, since that is what is fated to happen.
Determinism states that human action is dictated by prior causes that we have no control over. I may not have given you a thorough enough explanation before, but do you see the difference now? A determinist would say that choices still matter, even if we do not consciously author them or take responsibility for them. A classic way to confuse determinism and fatalism is to say, 'Why not just lie in bed and what will be will be?'
If you instead tell me it will lead me to have a strong inclination for choices in my life, then I still have my free will.
It's not a mere inclination. The entirety of who you are can be reduced to genetics and environment, which you have no control over. Therefore, those things determine all of your choices and actions. Indeed, even if you believe in a soul you still cannot refute the argument, since you would be no more responsible for the soul you are born with.
I will watch the video soon but I'm finding it fun to discuss beforehand for some reason even if it does lead to embarrassment on my end.
It won't lead to embarrassment. It isn't necessarily an easy concept to come to grips with, nor are people enthusiastic about accepting it.