I think that quote doesn't make any sense at all. It is basically telling someone that your problems are trivial and don't matter. You should be putting other people and their problems first. I find that notion to be a crock. I find that our society, North American for example, that we told to suck it up and be strong. Mask your problems and put them aside.
"When you can't be strong for yourself... at least be strong for the ones that need it the most."
Masking your problems and putting them aside is a load of crap. Doing that can be bad as you might blow up and hurt the people your care about. Never let those problems and emotions sit there and fester. You can deal with those problems and emotions while you keep living life. It is okay to say that you have problems and need help.
Our North American culture has dictated that we should not have problems. We should not be weak. That is not the way life works. Not everybody has their life together. A lot of people have problems and struggle to live day-to-day. This idea within North America of "be strong, not weak" is a crock.
Putting up a front is worse than anything. It shows we have to fake being strong before we should fix or attempt to fix what is wrong with ourselves. Putting up a front is an antiquated and archaic notion. If I had to be strong for someone else, I wouldn't necessarily do it. It would rather be up front and tell them that I have to fix what is wrong with me I do have things I need to fix with myself. Everybody does.
You don't need to mask your problems. You don't need to put a veil over your problems because I wouldn't expect you too. I'd hope you wouldn't expect me too.
If you are dealing with some issues, peace be with you. May you find the strength to persevere and move on with your life and away from these problems.