Without knowing much about your son and not being an expert on this, I say push to skip kindergarten. I'll try and summarize our situation and why I feel that way.
I have a 5 year old son in kindergarten right now, but I asked for him to skip into 1st grade at the beginning of the school year. Obviously they said no. I guess we were lucky to even get him into kindergarten at 4, but I felt that he wouldn't be stimulated given their curriculum. It's not that he was doing really advanced things yet, I just knew he was extremely curious and smart. They assured me he would be academically stimulated (without having met him) and social this and social that... So I said fine.
Turns out this school is absolutely amazing, his teacher, the principal, the district executives, everyone just really cares. My son enjoys school (it's only a little over 3 hours long including 2 recesses and lunch though). He does learn some things in school, like facts about plants and animals, telling time, money, etc. But I chose to enroll him in an after school academic program called Kumon to get the 1 hour/day academic stimulation I wanted for him.
He's done extraordinarily well in Kumon as he's literally gone from 1+1 in math to where he'll be doing calculus in several months. He's starting 4th grade reading, so not nearly as advanced as math, but nevertheless we are extremely proud of our boy. However, he still behaves like a kindergartener. So focusing, sitting still and just getting his work done can be very challenging.
So why do I feel you should push for 1st grade when my son has had a great year with an incredible school and astonishing academic achievements while going through kindergarten? First, after having read many studies on brain development, I'm a big believer in stimulating or exercising your mind at an early age. So your son will not get that in kindergarten to any great depth. And if you supplement his education (particularly easy if kindergarten is only 3 hours) like we did, then you just make it more difficult to be stimulated the next year.
I also feel social and behavioral development in kindergarten is overrated. Sure, it's helpful and our son has formed great friendships, but we can get that through playdates and being with older kids as well. Behavioral development is hard to push, it just comes with age (we hope). And kids will behave like the kids around them. I'm not worried about our son being around older kids as he progresses through school. For all this talk about social needs, schools really are mostly about academics. As far as dating and friends your son's own age, nothing precludes that outside of school. High school and then college sports will be an issue, so you have to ask yourself how much that matters.
Our son is still only in kindergarten and we don't have older kids to draw experience from... so I'm open to being completely wrong about all this :). Those are simply my thoughts given where we are today.