Stay at home parents

So me and my husband are both on parental leave and we are trying to decide who's gonna go back to work and who's gonna be the stay at home parent. Our baby is 8 weeks old. We both make about the same salary, but I honestly it's not really about salary. Most people think I should stay home because I'm the mom but its more complicated then that. We plan on also homeschooling through Elementary school and honestly I think my husband would be a better fit foe staying home and raising the kids. I love my baby so much, but... I have issues with compassion and patience and affection. I am not a nurturing person. I'm very tough love and figure it out type of person. That's how my family was. We were never touchy feely. I have a hard time having compassion. If a kid is throwing a tantrum in a store my husband is the type to ask if they need help. I'm the type to think in my head that kids a fucking brat do something. I don't like crying, especially over dumb shit. I'm not mean or anything about it, I'm just not the best person to go to for comfort. I'm the person you go to for fun or to talk. Comfort is more my husband type thing. He raised 3 siblings since he was 7. I lack patience, I lack compassion, and I'm not nurturing. My love language and going out and doing something. I don't do the whole hugging kissing booboos type if thing. And I take care of our daughter and stuff but my husband comforts her when she's crying because I feel she feeds off my energy when she's crying because I hate crying.