One thing I love about homeschool is that on a regular basis my kids interact with and form friendships with kids of all ages.
The public school system has for generations been based on a factory approach. Kids are divided according to "manufactured date" and sent down the designated conveyor belt. (Watch this TED talk by Sir. Ken Robinson to understand what I mean. It's my favorite! Or the shorter, animated version here.)
In my observation, kids in public school interact almost exclusively with kids their own age, rarely looking for friends among the kids in classes ahead or behind them.
Even bullying based solely on what grade you are happens often. The best example of this to me was at my middle school. There was only 7th and 8th graders at the school. To be called a "sevey" by one of the 8th graders was a huge insult. The 8th graders would tease and harass the 7th graders all the time simply because they were one year younger. It's insanity! No one can control their birthdate (manufactured date) and it's not the most important thing about you!
In the real world, that's not how relationships work. Friendships begin based on proximity. In public school, that means it's based on age because that's who's in your classroom. However, adults become close with the people they work with, share a hobby with, go to church with, etc. Before adults decide to hang out they don't ask each other when they graduated high school. Hubby is 4 years older that me. One of Hubby's best friends is about 6 years younger than him. One of my best friends is many years older than me.
I realize that part of the reason for the difference between adult friendships and childhood friendships is that children grow, mature, and change so much in such a short time. For example, there's a big difference between a 2 year old and a 3 year old in terms of things like speech capability and vocabulary, gross and fine motor ability, and play style. And all that evens out once you get past puberty.
However, I think it's really beneficial for children to interact with other children of all ages. They learn so much from the example of kids older than them and they learn compassion and nurturing skills by being with the younger kids. I love that my kids spend so much time with their siblings and that they attend so many enrichment classes and park days that aren't divided by age.