So why are you bothered by what other people call themselves if you are happy with your lot. What difference does it make to you.
This question wasn't directed at me, but I'll answer it anyway.
I am very happy with my situation, and have never felt in the least conflicted about my decision to work. I spent my own teenage years wishing that my mum would get a job because she was clearly miserable at home, so I don't have any baggage from my childhood about working mums. My dd is happy and thriving, and we have always had a very close relationship, and we spend lots of tune together. I'm also fortunate that DH and I both have extremely flexible roles, he pulls his weight at home and we have never had to depend heavily on paid childcare - we did have a nanny for 3-4 hours a day when dd was a baby but we haven't used any paid childcare since she started school six years ago. I never miss assemblies or sports days, can work from home if dd is sick.
I am the main breadwinner in our family, so haven't ever really had to consider the option of giving up work, but I really don't feel that I have missed out at all as a result of having a job and I wouldn't choose to give it up if the opportunity arose.
However, I think the terminology does matter. I think it matters immensely, because although it doesn't affect me directly, I see the impact on other working mothers - including some of those who I line manage - who do feel guilty and conflicted about the time they spend in work. Women who are absolutely bloody fantastic parents, who beat themselves up about not conforming to the expectation that mothers should want to devote their entire lives to their kids. Women who would love to stay at home with their kids but instead work incredibly hard in paid employment because they need to put food on the table. Women who are doing a fabulous job of raising fabulous children, who end up feeling inadequate as parents because they aren't present for every second of the day.
The men that I line manage don't experience this guilt or these conflicts in the same way, because to a large extent, society doesn't judge fathers for going out to work. Many women do feel judged, and I think that the terminology feeds into this. People may not intend to offend, But inherent in the notion of a "full-time parent" is the suggestion that other parents are not full-time. The unspoken implication is that those who go out to work - the part-time parents - are somehow lesser parents than those who stay at home.
At the end of the day, I respect the choices that all parents make about the balance between family life and paid employment. I accept that some families feel that having a parent at home works better for them. Personally, I would not use the term "unemployed" because I know that many people feel it misrepresents their situation, and I respect that view. However, I will continue to argue against any terminology that I think fuels the guilt that so many working mothers feel, because our use of language is what helps to shape our understanding of the world.
I have a daughter. I don't know what she will want to do in the future, if and when she has children of her own. She may want to go out to work, she may want to stay at home and look after them. Perhaps she will end up working at home, only time will tell. I would like to think that she will not feel judged or guilty about any of her choices. In the meantime, I will try to ensure that she isn't exposed to language that is loaded with value judgements.