There's a big difference though.

Saying that a president is not "your" president is political rhetoric.

If the defeated candidate alleges voter fraud that would invalidate the election and there are some "alternative" electors voting someone is trying to game the system. https://twitter.com/BretWeinstein/status/1338903265849708544

Say what you want about Hillary Clinton, but she made a public concession speech the day after the election, acknowledging she had lost.

There's a difference between contesting the moral legitimacy of a president and refusing to recognize they won. Republicans contested Obama's moral legitimacy for years but never to the point of alleging he had cheated and that the election results weren't valid.

Were there people who made arguments about the legal legitimacy of the elections of both Obama and Trump? Sure - the "birthers" alleged Obama wasn't a natural born citizen, and on the other side people spread some conspiracy theories over Trump being a "puppet" of Russia.

Again there was a major difference: the "birther" conspiracy theories was supported by many major figures (Trump included) and pursued even in the face of clear negative evidence. The "Russian puppet" theory was the purview of a minority - more serious concerns were investigated.

But that's beyond the point - an important point that both theories have in common is that they are about alleged legal issues of the candidate, not about contesting the legitimacy of the electoral process itself.

Moral legitimacy is ultimately a matter of opinion - you don't have to like a president just because they won. Legal legitimacy of the candidate is something that be ascertained, even if at a cost, without compromising faith in the institutions.

Alleging fraud is much worse.

Alleging fraud isn't just about the candidate you dislike being despicable or accusing them of being illegitimate. You're ALSO accusing the entire electoral system of being illegitimate - ultimately rejecting the electoral process as a whole.

An allegation of fraud is a VERY serious claim - much more serious than the candidate not having the right qualifications, or the candidate enforcing the will of a foreign power. By alleging voter fraud you're putting the entire system of democracy into question.

So if you allege fraud you'd better have overwhelming evidence that it happened - evidence that courts will just have to accept. Alleging fraud also accuses hundreds, maybe thousands of people, and several major institutions, of several negligence at best and connivance at worst.

What's even more troubling is that loyal Trump supporters have gotten some "alternative" electors to send votes claiming some states won by Biden for Trump - that's not just an accusation, it's deliberately subverting the system.