I agree with @Betty "mental" or "psychological" fits the criteria for
精神 in this context. When dealing with relationships it's typically mental or psychological interaction rather than a spiritual one. You think about how you will have good relationship, you don't believe that you will.
Hudong.com refers to
Which, in short, refers to a demand on one's mental state.
E.g., you think about how to have a good marriage, you don't believe that you will.
需要 I think "requirement" might also be appropriate in this context compared "need". The context of the sentence can suggest that this is something that must (required to) happen rather than something that should (need/want to) happen.
Requirement: I think when expressing
需要, "requirement" more appropriate than "need," especially when expressing the need to process certain credentials or characteristics.
- I.e., You must have something to happen in order to move on.
- E.g., In the US, you are required to be at least 18 years old in
order to be able to buy cigarettes.
Need: I think "need" would be more appropriate at emphasizing the level of (personal) passion or feelings.
I.e., You want something to happen in order to move on.
E.g., The sign needs to be red in order to mean "stop."
I would personally translate the sentence to something along the lines of:
Establishing good/favorable relationships between fellow members of (human) society is a psychological requirement for better mental well-being/health.
I used both psychological and mental in my translation, because I feel that
精神 has a broad range of meanings in English. I believe that here it implies both a psychological requirement (to be enforce a societal rule) for the benefit of better mental well-being/health or state of mind.
In order to get rid of the bit of redundancy between
人际关系 I bundled then into "relationships between fellow members of (human) society".