In total war situations where fighting is absolutely everywhere, it makes sense to give women a gun (in fact, it may make sense to give older kids a gun too)--because the war will come and find them even if they are not looking for it.
Where fighting is "organized," there are a lot of reasons why most countries are very reluctant to put women into ground close combat, one of which is that before you know it, you can end up with young women behind enemy lines. Their birth control will probably be thrown away or removed and there is a high chance they will be raped. Then you've got pregnant women behind enemy lines. Then you've got mothers and babiesbabies that are your country's citizensbehind enemy lines....
Another issue is the incredible amount of stuff that infantrymen and the like have to carry. I am told that a 70 pound pack is considered light. Now imagine carrying that and marching for hours....and running...and carrying said pack above your head while you wade through a river, and then somehow scrambling up the bank on the other side with it strapped to you. Now imagine that the guy next to you is shot and injured and fallssomehow you have to carry or drag him out of dangerwith his pack laced to him--while also carrying all your own stuff, ideally with one arm so that you can cover fire with the other arm.
Not easy for even a very fit woman.
Women are also much more likely to suffer severe injuries than men--physical and psychological. Catastrophic injuries to the skull, neck, spine and whatnot happen much more easily in women. There is also strong evidence that women are more likely to develop PTSD when exposed to the same level of combat stress. When people get badly injured like this it is extremely expensive for the militiary and society to deal with.
War requires loads and loads of work that is not ground close combat--admin and driving about and medical stuff and of course carrying on all the economic activities that still need to go on (and that includes household stuff, food prep and caring for children and elderly). I doubt we will ever see countries choosing to put women into ground close combat no matter what the situation, because in a war there is always so much work to do (most of it not direct combat) and it nearly always makes sense for women to do that instead.