So he's uncomfortable around large crowds. It is a big deal. Some people have social anxiety. Maybe that's not the case in this instance, but it should not be dismissed so flippantly.
As a woman who doesn't believe in marriage, I can only speak for myself, but I don't believe that my commitment can only be trusted if it's in writing. If I give my word that I'm going to do something, I'm going to follow through. After knowing someone for a while, it should be easy to tell whether a person can be depended on to keep their word. Based on that, the decision whether or not to believe what they say can be made. Marriage is more about the flaunting of material wealth. Don't believe me? How many shows are on TV about expensive weddings? Not all weddings are like that, but some of us don't need a ceremony to know that we're not going to fuck other people, etc. It actually doesn't prevent cheating at all. Many marriages end based on infidelity.
From what I understand, OP didn't say he doesn't feel strongly about marrying her. He said he doesn't feel strongly about marriage, period. He shouldn't get married if he doesn't want to, just like she should shouldn't stay with him if getting married is such a big deal to her. In my opinion, it's a stronger commitment to stay with someone without being married. If you stick around, even without a contract, you are really committed. There's nothing saying you have to stay, but you choose to. Remaining unmarried doesn't cause infidelity, just like marriage doesn't prevent it.
Security in a relationship doesn't come from marriage, it comes from trust. If she doesn't trust him, they have nothing.
A relationship involves two people (more if they're polyamorous), and both their opinions should count. Saying he would marry her if he loved her is bullshit and nothing more than a guilt trip. Emotional blackmail is a slippery slope...
