1- He has an omiai prepared.
2-He wants to take Maya back to where he lives (Where did he come from?)
3-It's the first time he sees his son that serious and he wants to ''bully'' him cause he loves him a lot (like father like son)
4- It would be freaking cliché but the father can also be gay, and he knows that when a relationship goes by hard times, they have more meaning as a couple.
5- *Insert your alternative opinion*
I also thought about those possibilities. It seems that there's a lot of people who are thinking the same reasons that you've listed and I like it. It was mentioned that his father was living in Sydney, Australia and taking care of their business. So excited, this new volume deals about family issues. Whatever the reason was I hope Maya-Nemu stay together.
Maya's dad was not giving me a feeling that he was really a strict parent who hates Maya-Nemu's relationship instead I'm getting an idea that he was up for something. What's happening right now might be a challenge to Maya to show how serious he was on dating Nemu. Maybe his dad was just testing him because up until now we didn't know the reason why his dad suddenly showed up and there might be a reason behind it.