I won't try to convince anybody with the goal of getting them to meditate. When people are given something with any degree of force, they usually won't bite. What I do, however, is inform rather than convince. I just say what meditation does for me and how I think it could help other people. It's up to them to pick it up or ask me further questions. But I only do this for people I think are genuinely interested. You have to have a bit of knowledge about people. Some may be scared off meditation (and Buddhism) for the rest of their lives if they do one meditation session that annoyed them. For them, it's not the time.
For others, it may just take a while. I have a friend I've known for many years, and I often told her how meditation helped me and what it does. I said it might also help her a bit. For example, when she was getting all messed up because of not being able to rest her mind. But I never did that with the intention of convincing her. It was up to her to figure out for herself whether she wanted to do it or not. Also, I trusted the results I had from meditation would show through my character. For about five years, she never took it very serious, and never meditated. But recently, she told me she hooked up with a meditation group and is having nice results already. I also gave her some Buddhist books to read and she liked them.
So, like a shy animal, you lure them instead of pushing them. In a way I find it quite amazing how many people have some sort of hidden desire to meditate, but never got to it. But if you bring it like an evangelist, you might ruin this hint of desire the have in them. Perhaps that's why the monk told you not to convince people.
In my family, I gave my parents some books on Buddhism and told them a bit of the basics and why I like it. They seem to be interested, which surprised me quite a bit actually. I'm convinced also here it is my actions that speak and not my words. But I feel it's not the right moment for them to try meditation. At least, not with me as the one who makes them try. People have to come from their own desire to meditate, or it is bound to fail anyway. They'll start off with the mindset "(s)he made me do it, but I don't want to. I'll just sit it out". Of course, such a mindset is a guarantee for failure.