I had an adult beginner rider not that long ago, she did maybe 3 lessons..she was absolutely terrified of horses. Not sure why she rode..or wanted to, but I spent those whole 3 lessons with her just brushing and walking, on the lunge line..on the safest horse we have (on the lunge line, he's pretty safe off of it too though) I mean, seriously, this horse got stung in the neck by a bee and didn't react on the trail. But anyways, I pushed her to do things, such as riding with her hands on her head, but at the speed she was comfortable at.
If you're not comfortable with cantering, don't do it. There's also an older lady who leases the oldest horse in the barn, and spends majority of her time walking and lightly trotting him. She used to take lessons and we had to force her to canter, and then one day we just quit. She doesn't want to show, and she wants to ride for fun, what is the point in pushing her to do something she is not comfortable with when she is perfectly happy walking, trotting, grooming, and spending time with her horse?
I have one lesson now, her second was tonight, that I don't imagine will be off of the lunge line for a long time. She can't seem to figure out posting, doesn't have a very good sense of balance, and I'm not comfortable letting her control the horse at all (even though the one she'd be on in that case just goes around no issue, but she's very very tiny and he's huge).
I've learned over time that there's a time to push, and a time to sit back and let people recover, especially if they mention to me that their nervous. Take a few weeks, build your confidence again, and then try.