There isn't a foolproof answer to this question... Personally, i have never tried to convince anybody to invest in anything. Not my parents, not my brother, not my friends...
If it goes wrong, they will always feel like you were responsible for their loss, and that's a burden i don't want... But that's just my personal opinion.
I've read through all the replies and although there were different responses, I think I have gotten the best answer to my question because most members gave similar answers.
I was not trying to convince my friend, I just educated him a bit on the difference between Bitcoin and altcoins. I don't convince people to invest in anything at all, not even Bitcoin.
From the replies, I think I would just help him understand Bitcoin better and leave the rest for him. If he wants to buy then fine, if he doesn't, still fine.
You made the correct decision; pressuring him to purchase Bitcoin even with a small percentage of his life savings could have ended awfully badly. You'd be the one to blame in case anything happened. Your friend could freak out and sell at a lower price, and you'll always have on your mind that you introduced him and is likely to blame you for his misfortune. I tend to avoid cryptocurrency discussions with any friends or acquaintances for this exact reason, because the discussion always leads to financial and investment advice I cannot provide. I wish I had a secret formula to turn rich, but I don't.