The Houses originated very early in the development of Horoscopic Astrology. The most used system is the twelve houses or places (Dodekatopos in Greek) But there was an alternative system of eight houses or places (Oktotopos) for a time. Both shared the same allocation for the fourth house. It was the House of Parents. The House of the Home and the House of the City (country) and for some The House of Mystical Matters. Those were the 'topics' that it covered.
You will notice that it's 'parents' not 'father' or 'mother'.
Now rachelcat is probably correct to identify patriarchy as the reason why it became to be identified with the father, when only one of the parents was being considered, and the mother became associated with the tenth, which by derived houses is the seventh house of marriage for the person signified by the fourth house. Certainly by the early medieval period and probably the late classical period, the fourth was seen as the House of the Father and the tenth as the House of the Mother. It remained so until the mid twentieth century.
As rachelcat points out the then modern approach began to reverse the association but did so on the basis of it's view of Cancer as the fourth Sign. The link between Houses, Signs and Planets as seen by the psychological view is both historically and theoretically incorrect. Houses are linked to the Ascendant, which can be in any sign. The Moon might rule Cancer but it hasn't any natural association with the fourth house. In the Thema Mundi, which was a hypothetical birth chart for the world, Cancer is on the Ascedant (So the Moon, has a natural association with mundane affairs and is used in that contex by modern Astrologers).
An older system of Planetary Joys associates the Moon with the third house - the House of the Goddess.
Now there is a natural association of the Moon with the mother, but also with the wife and any mature female. Venus is associated with younger women but can stand for the wife in certain circumstances.
So which should you use?
I use the fourth for parents (both). If I have to differentiate between the two, I try and look for the circumstances. For a single mother, I'd use the fourth without any question. If the mother is the main wage earner and supporter, I'd also use the fourth for the mother. I'd use the fourth for the mother in a matriarchal society. But for most of the Western world (and indeed the world as a whole), patriarchy still reigns. So if I have to consider the two parents separately but need to refer to both, I'd use the father for the fourth and the mother for the tenth. In the event of having to consider one parent only (either mother or father) there's a very good case for using the fourth for that parent. The Hellenistic assignments did not put the mother in the tenth or only the father in the fourth.
It is true though that Hellenistic society was patriarchal and they rarely considered the mother on her own, unless she was very important, such as a queen (in which case she got the third by virtue of her royal rank).