its the societal norms. some manga still stick to the idea that straight relationships are the standard, where male alphas are supposed to match up with female omegas. being a male omega might get stigmatized or frowned upon in these stories because they're pretty rare and don't fit into the traditional gender roles
My personal catch in Tadaima, Okaeri omegaverse is that Omega are considered to be people who can't advance into higher societal class because of their body constitution. Since only Omega have sexual pheromones that can trigger Alpha's animalistic instinct, Omegas are considered to be "hindrance" in society. Which is why people believe that Alpha should only be with Alpha, and Omega should only be with Omega (Alphas can get pregnant here, hence Matsuo's parents). So the problem in this universe is not in the primary sex classification like male Alpha supposed to be with female Omega, but more about the nature of the secondary sex of Alpha, Beta, and Omega itself.
To answer your question, mating of Alpha and Omega in this universe is often looked down upon because of the difference in their social standing and also because of the "ownership" nature of a bond which makes mated Omega can only rely on their Alpha for the rest of their life while Alpha can mate with several Omega if they want to. This is very disadvantageous for Omega.
Omegaverse is interesting because every author can create their own rules regarding the Omegaverse so it's very versatile haha what applies to one story might not be the case in another.
I am little confused here. I do know about omegaverse but aren't alpha and Omega are supposed to be together? So why are they being frowned upon here. Is here some different rule ?. I am coming after watching the anime