Ok. As a woman, I will set the record straight on this.
1. Pads/tampons CANNOT be flushed down the toilet, they will clog it.
2. Generally, women will dispose of used pads/tampons in the garbage can next to the toilet. The reason being, when you are mid-change, it isn’t convenient to go all the way down the stairs, butt-naked from the waist down, dripping blood the whole way, to dispose of it in the kitchen garbage, or, even worse, the outside garbage can. And then back upstairs to insert a new one. Also, it is a terrible waste (and bad for the environment) to throw out an entire garbage can liner with just one pad/tampon in it. So that’s why we don’t throw these out after EVERY change. It’s not unreasonable to request that the garbage bin in the bathroom have a lid, so that you cannot smell it as much, and that it be emptied nightly. Additionally, if you place a sheet of Bounce (dryer lint sheet) under the trash can liner, you will not smell anything at all. TRUST ME. I live in a household with 4 women, 3 of them who menstruate, usually all at the same time (me and my daughters) and there is no smell. Just ask my dad.
3. It’s lovely that your lady uses a menstrual cup for you, but that is not a feasible option for all women. Women are not all shaped the same on the inside. Some women are simply unable to place it so that it remains put the way it should be. I, personally, have never been able to use a tampon in my life. It’s just an individual thing.
There, you have your answer, or at least a start. I would humbly request that you refer to women with a bit more respect; I realize you are annoyed and frustrated, but this didn’t reflect too well on you. Thank you.