Is it appropriate to say to your man:
"..if you don't want to get engaged after 2 years of dating, then I will move on."
I think the answer (within reason) is an unequivocal YES. I know many stories of women who waited around 5, 7, 10 years for their man to propose, and guess what, he kept saying he would, and he didn't!!!
Eventually the girl left, broken hearted with many wasted years. She had to start ALL over again after investing so much time and was that awful.
Don't let a man waste your time, silly girl!
If you are ready to marry, (and feel you know each other well and have dated extensively), if a guy wants to be with you, he doesn't need to throw the 1000 excuses book at you. What is also not very smart for women is to force/pressure/claw/whine their way into a proposal. This is also very silly. He may regret it later, and then you won't get the love you deserve, because it was under obligation.
Instead, if the relationship isn't going anywhere clearly - you aren't spending more time together, he isn't sure still if you are "the one" - then politely tell him that he can keep trying to figure it out, while you go on and find someone who is sure.
Most men would say ultimatums are a no-no. Men do not want pressure, they will recoil like a snail into their shell - the shell of non commitment. Instead, you should communicate to him openly how you feel about the situation in a non threatening, non bitchy, and mature manner. He will respect you for this approach.
If you check the relationship meter - as in, when you ask him if he wants to commit, if he isn't sure girl, don't stick around for too long.
Sure, there may be some people who are fine with never marrying, but if you are not that person, then make sure you don't stay with a man who feels this way.
My heart goes out to you lovely ladies.