With regard to 2nd graders, I don't get the inter-sports for them. Everyone needs physical activity that they enjoy. I have seen parents and coaches get all bound up in a game, softball, soccer, football. It's an ego thing for the parents and something they really need to have a real moment with to identify that and resolve. If nothing else to assure that they aren't in some way living vicariously through their children. And we've all been party to a set parents like that once in our lives at least.
When it comes to sports in general for girls/women-I'm all for it. I was a basketball player in high school and played it the first year of my undergrad. And loved it immensely. I started playing when my father, his mother and my sister would meet outside by the garage and play and I was steadily beating my dad who is a phenomenal player in many aspects. (He played for the St. Louis Cardinals for 1 season before he blew out his knee). My maternal grandmother was mind blowing and she taught me moves that carried me far in my little high school athletic career. She was all star in her state in 1940, 1942 and 1943. She was tall, beautiful, charming and simply lovely in every way.
After my transfer to a different school they did not offer baskeball but lacrosse. And I played marginally well most I had to show for my efforts were bruised, injured shins, shoulder from fall and frankly a ton of mean girls. But I didn't go to that school as a transfer student for athletics but for it's academic rigor.
Today, at a very old 40 (I can not believe it!) I am a marathon runner. I used to do triathlons but realized that I didn't enjoy it anymore so scaled back. Today, I run about 3 miles a day which isn't a lot. I used to run about 8 miles per day. But I have a life so something had to give.
Am I a modernist because I exercise? No. I enjoy the physical activity. I do get a lot of benefits for my activities. Mainly the ever present (and sometimes difficult to attain) 'second wind' which is addictive. I generally can eat whatever I want without worry. Though as I'm aging I'm noticing it's not as forgiving as it used to be, so sooner than later I'll be modifying that last sentence.
If we lived in a time where physical labor was part and parcel to our survival I can guarantee you me running just for the 'fun' of it wouldn't be happening. I can venture a guess that the reason there is this type of physical activity in women (and men) is primarily because we are hard wired to be physically active in some aspect. Most people are not from an aristocratic background and farming or a type of trade was all manually intensive. Coming from farming communities such as myself I loved farm work and miss it in a nostalgic way. Living it wouldn't be my cup of tea right now simply because I have become accustomed to what my life is now.
If you feel guilty about being around these children doing this could you perhaps request a different venue or age/gender group? I don't think you're sexist at all. I think your a kind, sensitive person who is protecting his self, his soul. Many hugs to you, sweetheart.