[My baby Milo]

I took Milo to vet to get his shot, anal glans express and his toe nails clipped. I haven't had his nails cut in about a month so they were long. The vet cut them really short and they bleed. He said that the quick has grown out to long so he needed to cut them back. Not all of them bleed but i was kinda mad because I thought he was cutting them to short. Does the quick grow out that far? I haven't had that to happen before.