Some dogs don't like their nails cut, not because they've had a bad experience, but because you are hanging on to their leg, especially their front one. In the wild, when one dog defends its territory from another, they fight and what they do in their fight is try to break or injure the leg (usually the front one) of the other dog. If one dog can injure or break the leg of the other, then the other can't hunt and therefore can't survive. When your dog struggles from you holding its leg (especially a front one), he is not misbehaving ... he's acting on survival instinct and he really doesn't know why (he just does it - it's genetically in them to protect their legs).
When you insist and hang on tight and they stuggle hard, they will poop (sometimes diahrea), and sometimes bust their anal glads (excrete the smelly stuff). Even worse, while the dog struggles, if you cut a quick and the dog smells blood, you are going to have little chance calming him to finish the rest of his nails. They have very good noses ... one sniff of blood will panic them. You will then definetly have difficulty doing his nails in the future. The anal gland smell has left an impression on your dog too. Other animals, when they smell that much glandular excretion, will interpret it as the smell of fear, and they'll get suspicious, or eat it (domestication sometimes rules). If after excretion, the dog is not washed & rinsed off, the contents excreted from the glands are very potent and irritate the skin a bit, which is why the licking (or he's trying to eat it - domestication again).
My suggestion is that you have a groomer do your dogs nails next time. They have techniques & experience. It might be better that way for your dog. Or, have a groomer show you how to do it so as not to get into a struggling match with your dog. And learn how to express those glands too, it's real easy once somebody shows you how to do it.