The alternate that "you are allowed to show your feelings" is trying to combat, is the idea that you can't show your feelings to anyone, at any time.
So your advice is correct, but nowhere near the issue yet. You're telling people when to shift into fourth gear, when they're struggling to get out of first.
I disagree with both. Expressing your feelings is a part of good communication, and feeling free to express sadness or frustration as needed is how you stave off the kinds of arguments and blowups that have much more severe consequences.
But that is act, not emotion.
This is a cornerstone of Cognitive Behavioral Therapy, which is, in short, "I am free to notice that when this happens, I feel this certain way, and that usually relates to these outcomes. How can my behavior influence this in my favor?"
You should not show your feelings to just anyone. You should have self worth and share with those you trust. There is a reason why PR exists for people in the public sphere. Most people will treat you kindly and it is important to remember that, but a good lesson for the internet would be to be keenly aware of the pitfalls of sharing too much and that includes your feelings very often.