It is true to an extent, because you can't really draw a line between nature and culture. I don't think there's a definite answer to this question, but I'll try to share some theories around it.
From an evolutionary point of view, female hominids have always invested a big part of their time and energy in their offspring's survival. Our babies take a very long time to develop, and they do it outside the womb (because the hominid brain is so big, it needs to keep growing after the infant is born, otherwise it won't fit through the pelvis).
African hominoids, including chimpanzees (Pan troglodytes), gorillas
(Gorilla gorilla), and humans (Homo sapiens; Gagneux et al., 1999),
share a number of parenting mechanisms with other placental mammals,
including internal gestation, lactation, and attachment mechanisms
involving neuropeptides such as oxytocin.
Geary et al., 2001
Early hominids combined hunting and scavenging, and used mostly scavenging because they were competing with large predators (this article by Mark Fox expands on the subject).
Scavenging is something a female hominid can potentially do while carrying an infant, while hunting would be technically impossible until the baby has grown up. This doesn't mean males went hunting and females stayed in a cave feeding their babies 24/7, it just means a more balanced distribution of tasks would mean more chances of infants living up to adulthood and reproducing.
A lot of factors played in this subtle 'evolution' of families and groups. Charles Darwin (1871) was the first to propose that competition for mates plays an important role in reproductive success (he called this process sexual selection). Stronger males have an 'advantage': they can protect their group and offspring against other groups and against predators more effectively.
Intergroup conflict is undeniably pervasive across human societies
(...) There are reliable accounts of intergroup conflict in past
hunter–gatherer societies—usually via raiding and ambushing—killing
substantial numbers of people.
McDonald et al., 2012
Now, a larger / taller man may have been able to provide more protection, have greater genetic qualities to pass on to their future children (or look like he does), and even be awarded with a better social status. But we can't talk only in biological terms, because we are (also, or mainly) cultural beings. The previous seems valid and proven for hominids, but what about modern Homo Sapiens?
Through studying group structure and complex social relationships,
we've learned that human ancestors may have acted similar to primates
-- grooming and all
We can't be absolutely certain on how these behaviours have changed during our evolution as a species, but we do know culture and language have played a major role in how things developed.
Culture mediates our relationships with other people, with the
environment, with spirits and deities, and with abstract or imagined
worlds like mathematics and the future. Culture provides the context
for language, without which our ability to think would be grossly
constrained (however often we find ourselves at a loss for words), and
it makes possible our endlessly diverse modes of social cooperation
and conflict. Culture encompasses much of what makes us distinctively
There is a consensus that through evolution, female hominids seem to have sexually selected stronger males as mates. There is also a consensus that primate behaviour studies can shed some light not only on how our ancestors lived, but also on our species as it is now.
The moment we start talking about culture, these extrapolations become extremely complex, and our current tools not good enough to deepen them. While some biological pressure might still exist, what was once considered a good mate has drifted to a whole new set of characteristics. Being protective can now mean having resources, having money or being a position of power.
In order to optimize their inclusive ﬁtness, women may look for a man
who is relatively older (and has thus had more time to accrue material
and political wealth) and of high social status. It should be noted
that these preferences are not always at the conscious level, but are
theorized to have been ingrained into the human psyche as innate
responses through the process of evolution.
Braun & Bryan, 2006
Pawlowski, B., Dunbar, R. I. M., & Lipowicz, A. (2000). Tall men have more reproductive success. Nature, 403, 156.
Nakamura, Michio. "'Gatherings' of social grooming among wild chimpanzees: implications for evolution of sociality." Journal of Human Evolution. 44, 1. 59-71. 2003.
Braun, M. F., & Bryan, A. (2006). Female waist-to-hip and male waist-to-shoulder ratios as determinants of romantic desirability. Journal of Social and Personal Relationships, 23, 805-819.
Gills, J. S., & Avis, W. E. (1980). The male-taller norm in mate selection. Personality and Social Psychology Bulletin, 6, 396-401.
Fink, B., Neave, N., Brewer, G., & Pawlowski, B. (2007). Variable preferences for sexual dimorphism in stature (SDS): Further evidence for an adjustment in relation to own height. Personality and Individual Differences, 43, 2249-2257.
Buss, D., M. (1998). The evolution of human intrasexual competition: Tactics of mate attraction. Journal of Personality and Social Psychology, 54, 616-628.
Pawlowski, B., & Jasienska, G. (2005). Women’s preferences for sexual dimorphism in height depend on menstrual cycle phase and expected duration of relationship. Biological Psychology, 70, 38-43.
Note: This is my first answer in Skeptics, please let me know how I can make it better!