What does it mean when someone says "I just need some space"
How long is a piece of string? "I just need some space" certainly can be a euphemism for "I don't want to see you any more", but to always assume that would be to see only the shadows in a picture.
It could be that when someone asks for space, that's exactly what they want, while still having strong feelings for you and wishing to continue the relationship.
Supposing 'I want some space' really does just mean that someone would like a little time alone, how can you make sense of that? One thing it can be helpful to understand is that someone's wanting some space may have nothing to do with you.
Besides enjoying time alone being a totally natural thing, there could also be stresses or pressures in other parts of life, and having time alone just provides a way for that pressure to be released or come to terms with. It's not necessary to see that as a rejection of support. Instead try to understand that in that particular instance that person's needs were best met by spending time alone. Other times in other circumstances they may really appreciate your support. Acknowledging this makes for more robust relationships.
If someone would like space because they want to think about how their relationship with you is developing, again this can be understood as a completely natural response that doesn't necessarily suggest any shortcoming in you.
Some people, due to past experiences, are especially cautious about getting emotionally close to others, or they have some difficult circumstances in their life that makes them hesitant or doubtful about a relationship, or they have a low self-image and don't want to risk rejection further down the line. There are many possible reasons, besides someone losing their feelings for you.
In any case if someone is already feeling stressed or anxious about what to do, pressuring them to ignore their desire for space probably wont help anyone. Instead, be clear about how you feel in a way that doesn't lay responsibility for your happiness on them. Offer what you'd like to share and then simply give them the space they want. (If your feelings change in the mean time, you can always let them know.)
How can you tell what kind of 'I need some space' someone means? By talking about it in a way that invites honest sharing, rather than defensiveness. If someone perceives little risk of blame, or being made to feel guilty, or that they're somehow responsible for your feelings, then they're much more likely to open up and say what's really going on for them. Whatever the issue, whether it directly involves you or not, there is then the option of further discussion, with the emphasis on mutual acceptance and non-judgemental empathy.
"Healthy Loving Relationships" looks at the ways which pre-judging what someone's intentions or feelings are can cause problems, and explores more effective ways of connecting and understanding each other. A central theme is the transformative power of empathy to develop more fulfilling relationships and resolve conflict.