How do you tell if someone is emotionally healthy? Healthy people do not get upset when you share personal things (like how you feel, what you need, or what your reality is) because they know that those things are not statements about them, they're statements about you. They're information you're relaying about your inner world.
Your need to eat just means you need food. If you're thirsty, you need to drink, if you're tired, you need sleep.
I mention physical needs because it's very obvious that they are attached to the person who has them and not the person who doesn't, but this concept should apply to all needs, including those for closeness, distance, connection, downtime, intimacy, adventure, you name it.
Sometimes needs align, and that's great but often they don't. It's the handling of these differences that Carolyn Hax was referring to in the above quote.
Healthy relationships do NOT need both partners to feel the same way all the time. What they DO need is communication -- regularly communicating inner state and reality, and receiving and accepting information as it comes in without reacting in a way that shuts down the input.
Differing needs can often be misinterpreted. For example, if one partner wants to read a book and the other wants to share a deep conversation, opportunities exist for misunderstanding.
The partner who wanted to connect might misread the other's need for downtime as distancing. And maybe the partner who wanted to read could misinterpret the other as being smothering or lacking respect for boundaries. Neither can see the full picture but each may feel hurt, making it even harder to see where each is coming from.
Empathy breaks down when we're hurt because our own needs (for validation, for feeling understood, for feeling loved, honored, heard, etc.) rear up and obscure incoming signals. Suddenly everything appears to confirm what we feel.
The brain is a wet, squishy pattern-detection computer which constantly scans the environment for signs of anything that it learned was painful. It does this to keep you safe but sometimes it is overzealous. If there's a history of feeling unloved or smothered (or whatever the strong emotion is), especially going back to childhood, this creates a hair-trigger sensitivity to even the slightest perception that it may be happening again. This is just your brain trying to protect you, but also why something that was painful before may keep stinging until you relearn the things which no longer have the same meaning they did last time.
This is where skills in emotional regulation are handy, because it means you'll be able to refrain from acting on those feelings in an outburst until you can understand what parts of them are related to old pain and what parts are related to what's happening right now.
I believe this is what's happening for people when they can't receive your truth without getting upset -- it's triggering them somehow. There may be something in their history that comes alive. But this is useful information when choosing your tribe.