I think it comes from that gay men are more likely to have taken a step away from toxic masculinity than straight men (please note the emphasis). Obama is not incorrect that having gay men as friends can, then, help some straight men step away from toxic masculinity as well, and thus expand their sense of empathy and kindness, but the quote as it’s shown in the meme is insufficient and implies a more essentialist than cultural view of the behavior of homosexual men.

The quote could be out of context. Or Obama could just be showing his age - ultimately, he is definitely a man from a prior generation.