The phrase doesn't annoy me, but I do think it is completely meaningless.
For the phrase to have meaning, then it has to be used to differentiate mothers from other types of mothers.
Usually, the phrase is used to refer to mothers who look after their children 100% of the time. But then, what about mothers whose children who go to preschool or school? They're not with their children 100% of the time, so surely then they cannot be called 'full time mothers'. Yet women who do not work and have preschool / school aged children on Mumsnet still like to use this phrase.
Incidentally, when my DD got her 15 hours free at preschool, I put her in for 3 x 5 hour sessions and I worked at that time. So the time she was at home, I was with her (exactly the same as any other non working mother), now my DDs are at school, I work full time, but am lucky enough to work condensed hours term time only, so essentially I work when they are at school (I teach). So when they're not at school, I'm with them. So does that mean I am a full time mother? As there is nothing that differentiates a mother of a school aged child who does not work from me. But that would make me a "full time mother who also works full time" which is just crazy!
If you're going to use the phrase 'full time mother' then at best it can only be used for children up to preschool age 2/3, because then mothers stop "mothering" (to quote an earlier poster) full time, and they become 'part time' like every one else. Which just goes to show how meaningless this phrase actually is.
The objection to SAHM is often that women do not actually stay at home. Sometimes I wonder whether 'based at home' would be better, because that is where the woman is based during the day, even if she goes elsewhere. Shame it sounds a bit wanky
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