A very true line for the most part. Someone who loves you will almost never be able to make you cry and even if they do by any chance, their heart would ache to see you shedding even a single tear. Several of us would feel bad when we see someone crying in front of us, except if we are sadists or a nut cases. However what I am referring to over here, is seeing a loved one cry. There have been people in my life whose tears that I have witnessed still hurt me when I think of them. If by any chance it is my mom, I go completely paranoid, though she almost never cries.
Of course there is this other side to tears - False tears. Some people will shed false tears and get whatever they need. In my opinion the biggest betrayal is by someone who comes and sheds false tears in front of you, makes you emotionally vulnerable and gets whatever they want. Ideally when you see a loved one crying, you will feel really really sad and will want to do everything you can to console the other person. But it is ridiculous when someone exploits you with tears.
Now coming to cry for others. While it is common for people to cry over breakups or friends not talking to them or any such thing and people eventually do move on, but someone who is directly responsible for making you cry isn't a great person to have in your life. Some strong people try to control showing out their tears, but deep inside there is someone who is crying in their head. I have seen people who have made me cry and never bothered to do anything about it. It just made me shed more tears in the beginning and then realize eventually that such people are just not worth my tears. However I also have some people who totally shower me with their love and affection and can never ever see me shed a single tear. It is these people, I have realized are the ones who really care. Bottom line is when you give someone more importance than what they deserve, you are bound to cry externally or internally, which is just not worth it. Shedding tears for someone who really cares for you and who is in extreme pain means something. I used to be of the opinion that when you truly love someone, irrespective of how they treat you, seeing them in pain should bring tears on to your eyes. May be it is still true, may be somewhere in my heart I still feel so. But sometimes it is just totally pointless and worthless. Essentially I try not make anyone cry even by mistake, and try to make sure people don't really make me cry and eventually if I do shed tears for people I love and care about, I have learnt to try my best to forget those tears.