Okay here’s why you can touch a mezuza and not a sefer torah:
1 the sefer torah is holier than a mezuza or tefilin 2 the mezuza has a cover, one cover is enough for the mezuza. The cover of the sefer torah recieves a high degree of kedusha, its too holy to touch. Probably if the sefer would have additional coverings a woman would be able to touch it.
The atzei chaim, the sticks that you hold it with receive a very high degree of kedushah as written in the shulchan aruch, or hachaim 141.