Self defense and fighting in a combat sport are two different things. Most of the skills you learn in MMA are applicable to self defense. But there is a gap because of the focus on competition. How long have you been training? Have you fought at an amateur or professional level? How different are the two of you physically?
I don't know your skills, but you need to measure your own progress. Just because someone goes to train regularly doesn't mean they've gradually increased their skills over time. I have over four years of grappling experience, but I'm still a white belt. Part of that is inconsistent training due to life circumstances, but it's also because grappling is hard for me to learn.
Another thing to consider is that just because someone is untrained in technique doesn't mean they lack strength, power, reflexes, flexibility, and so on. One can't casually compare the skills someone may learn from another sport or fitness training, but most types of training have at least some benefit overall. Those things can carry over to other activities like combat sports even if the person is lacking in technique. We can logically assume a fighter punches harder than a powerlifter. But we shouldn't be clueless enough to think the latter has no power just because they lack technique. Most people can block and dodge punches without much training.
Training increases ones chances of success. It doesn't mean you'll beat everyone you encounter with less training especially if you aren't at an advanced level.