If I was going based on these trainers and was six months into training, lifting 120lbs would be a solid goal for a 3-rep set. Doing a full push-up would have me lifting about 180lbs from the starting position, and doing that ten times with good form is genuinely difficult if you don't regularly train for it.
It's also going to be more difficult for people who are fat, or who are top-heavy, or who are tall.
So "I am not focused on any kind of intensive lifting" is a perfectly valid response and please don't feel bad if you can't do ten push-ups, that shit is hard.
(If you want to train to do push-ups, the higher your hands are in the starting position the less weight you are lifting - start with wall push-ups then move to counter height push-ups then move to bench-height, then bent knee, then full push-ups. If you want to add weight, move your feet up higher and higher until you're doing hand stand push-ups. It's all leverage!)