My understanding of the research around personality development is that something like 80% (BS statistic I know) of the personality is formed in the first 5 years of development. The early few years are when we get conditioned with the core emotional programming: "I am safe" vs. "I am at risk" - "I am lovable" vs. "I am unlovable." etc. which plays a huge role down the line in lifestyle, relationships, and life in general.
Probably not a big deal whether it's the father or mother at the young age, but having adults around to be available to the emotional needs of the young child seems to be extremely important. Maybe easier to split the "full time job" of parenting in this critical period?
If you want to nerd out, check out "Affect Regulation and the Origin of the Self - The Neurobiology of Emotional Development" by Allan Schore