TL;DR: 110 m was set for historical reasons and women had the distance set to 100 m to both use metric units and keep consistency with the number of hurdles run by men (10).
110 metres hurdles in Wikipedia explains that the distance of 110 metres comes from a 120 yards standard defined in the mid-1800s:
The first standards were attempted in 1864 in Oxford and Cambridge: The length of the course was set to 120 yards (109.7 m) and over its course, runners were required to clear ten 3 foot 6 inch (1.07 m) high hurdles. The height and spacing of the hurdles have been related to Imperial units ever since. After the length of the course was rounded up to 110 metres in France in 1888, the standards were pretty much complete (except for Germany where 1 metre high hurdles were used until 1907).
My interpretation is that technique and spacing became so standard that changing the distance would have made it a completely new competition, hence it was kept.
Time passed and women's 100 metres hurdles appeared:
The Olympic Games had included the 80 m hurdles in the program from 1932 to 1968. Starting with the 1972 Summer Olympics the women's race was lengthened to 100 m hurdles.
The hurdles sprint race has been run by women since the beginning of women's athletics, just after the end of World War I. The distances and hurdle heights varied widely in the beginning. While the men had zeroed in on the 110 m hurdles, the International Women's Sport Federation had registered records for eight different disciplines by 1926 (60 yards/75 cm height, 60 yards/61 cm, 65 yards/75 cm, 83 yards/75 cm, 100 yards/75 cm, 100 yards/61 cm, 120 yards/75 cm, 110 metres/75 cm). At the first Women's World Games in 1922 a 100 m hurdles race was run.
The article follows with some interesting insight and follows with:
During the 1960s some experimental races were run over a distance of 100 metres using hurdles with a height of 76.2 cm. During the 1968 Summer Olympics a decision was made to introduce the 100 m hurdles using hurdles with a height of 84 cm and the first international event in the 100 m hurdles occurred at the European Athletics Championships, which were won by Karin Balzer, GDR. The modern 100 m race has an extra 2 hurdles compared to the 80 m race, which are higher and spaced slightly further apart. The home stretch is shorter by 1.5 m.
My interpretation is that they wanted to increase the number of hurdles to 10 but also keep the spacing. To do so they could just increase to 100 metres.
This reasoning is also followed in the debate 80 meter hurdles?:
I don't know why, but if, as you speculate, the aim was to harmonize with the men's hurdles, I think it has been achieved in the most practical manner. With the change, the women now face ten obstacles, just as the men do. Furthermore, by increasing the overall distance only twenty meters, the women can still three-step the hurdles, just as the men do. The key parameter is distance between hurdles.
I took the official spacing for hurdles and did some calculations to see what other combinations could have been used.
The total distance comes from:
start + (hurdles-1)*distance_hurdles + finish
so it is like this:
hurdles start distance hurdles finish total metres
80m (W) 8 12 8 12 80
100m (W) 10 13 8,5 10,5 100
110m (M) 10 13,72 9,14 14,02 110
If we were to have a 110m (W) with the same amount of hurdles, 10, it should be like:
hurdles start distance hurdles finish total metres
110m (W) 10 12 10 12 110
The problem is that the bigger distance between hurdles makes it hard to combine with the typical 4-step and may make them need an extra, smaller step that would break speed.
If we were to have a 110m (W) with similar spacing, it should be like:
hurdles start distance hurdles finish total metres
110m (W) 12 12 8 10 100
so this is completely doable and would make the distance equivalent to men's. However, it may be way harder since the amount of hurdles to skip is bigger.