I seem to have wrong math for marginal independence proof (details in question), can anyone explain where my logic went wrong.

Question

I'm not sure but for proofing marginal independence I've came across this stack exchange post, and from there to this link, where I found that the condition to hold for 2 variables to be independent marginally is $P(X \lor Y) = P(X)$ which I assume can be basically translated to the probability of either events X, or Y happening is identical to probability of X happening which doesn't make much sense. Like that would imply that $P(x) + P(y) - P(x)\times{P(y)} = P(x)$, which is only possible when $P(x)\times{P(y)} = P(y)$ which then implies that $P(x) = 1$ which implies X is certain. So for y to be independent of X, X should be certain? that looks like I've completely messed my math somehow