I can tell you right now its a boy thing. I can't do any activity without wanting to crush others. You'd rather appear to succeed by causing / encouraging / allowing others to do badly, than achieve an objectively better result by striving to be the best you can? Don't you see how self-defeating that is?
Perhaps you meant 'be better than', 'beat in competition' rather than 'crush'. You do see that crush implies harm? Perhaps you mean it mentally, you want to crush their egos? There's an implicit assumption there that their egos are as fragile as yours. Maybe they're mentally stronger, more mature, better people than you, so that doesn't apply.
If that isn't what you meant, just 'beat them in competition', using the competition to drive yourself to do the best you possibly can, then the word 'crush' doesn't fit, you'd be describing it in terms of your own achievement.
I've come across immature people in the workplace who think like this - that putting, and doing other people down makes them look better. They're anti-productive and a liability. Not successful people at all, because they can't inspire, connect and lead. Well, perhaps some gravitate towards fields where destructive behaviour is rewarded and, unlike in life, things are set up to appear to be a zero sum game.
In a sporting context though, where's the boost to your ego in 'crushing' someone from a different competitive category, who no-one would expect to be as fast as you? "Whoohoo, I can beat a four-year-old and a seventy-four year-old at the hundred metres, aren't I great!" No, you sound like a twat. That's why the DH competing against the OP would be so absurd - though it's not clear he's actually doing this. The 'we're blokes, we can't help it' explanation makes it sound like you would though!
I think if you both joined club(s) OP, you'd find your own people and get as much support or competition as you wanted. Your DH will quickly find people, in his category, who are faster than him (and who can't be 'crushed' however hard he tries). Might be good for his soul!
Top tip - if you can carry on running for long enough, enough other people drop out that you can do quite well in the 60+ and 70+ categories. Not crushing the opposition so much as natural wastage (mostly of knees, hips and motivation). Not an entirely contrived victory either, since carrying on running competitively at that age is something of an achievement in itself.