Sounds like he's having digestive problems! Poor child! He's probably having a lot of discomfort from the formula. And he's not getting enough to eat! He is ready to eat mashed up food.
I also have a question - what is wrong with him wanting to breast feed? That is the BEST solution. You can breast feed pretty much up to 2 and 3 years old like they used to, 100 years ago! Don't quit just because someone says you should. Did you know that scientific studies have proven that a) formula does NOT have nutrients like DHA and essential fatty acids that are neccessary for normal brain function? Also, did you know breastfeeding up to 2 years old - they have seen it benefiting brain health up to 2 years old in children!! That is also plenty of reason for you to continue - of course I would supplement with what I recommended below.
Try doing this instead (used previously for other food advice):I don't blame your 1-year old. Have you ever tasted baby food? It's awful. I think baby food teaches children to hate their veggies because it tastes so bad. Anyway, my grandmother taught me to cook potatoes and carrots, mash them up with a fork, with a little salt and butter, MY 1-year old LOVED it. He was so scrawny when I went to live with her, and she made this frequently, and looked much less scrawny after a month! You can actually do this with any veggie and potatoe. Also, I used to use my KitchenAid Mixer - it has a food grinder. I used to grind the food with it for my babies (AFTER it was cooked, of course). You can also use a blender or Cuisinart to mash stuff. It's a lot of work, but you're right, they can't chew very well yet. I pretty much mashed and ground anything I cooked for us.