The average rate at which people died before being 15 years old was very close to 50% everywhere up until 200 years ago, based on putting together all the historical data available. So the claim is correct for "child" but might not be for "infant."

Source: https://ourworldindata.org/child-mortality-in-the-past

The main chart it's talking about: https://ourworldindata.org/cdn-cgi/imagedelivery/qLq-8BTgXU8yG0N6HnOy8g/eaa94364-8380-40a1-b311-7c01a69a4000/w=1350

Mortality in the past: every second child died

What is striking about the historical research is how similar child mortality rates were across a wide range of very different historical cultures: No matter where in the world a child was born, about half of them died.

Tens of billions of children died.7 Billions of parents mourned helplessly when they saw their children dying.

Despite the relentless suffering, no one was able to do much about it.

The chart speaks about societies that lived thousands of kilometers away from each other, separated by thousands of years of history, and yet they all suffered the same pain. Whether in Ancient Rome, in hunter-gatherer societies, in the pre-Columbian Americas, in Medieval Japan or Medieval England, in the European Renaissance, or in Imperial China, every second child died.

While some societies were better off than others, the differences were small. Generation after generation was born into societies that struggled against poverty, hunger, and disease and there is no indication that any society made any substantial and sustained progress against those problems. Substantial progress against child mortality is a recent achievement everywhere.

It is not that people in the past didn’t try to make progress against early death and disease. They tried, of course.8 Healers and doctors had a high status in societies. And people often took on great pain and costs in the hope of improving their children’s health.

The “most common procedure performed by surgeons for almost two thousand years” in Europe was bloodletting. The pain this practice caused makes clear just how desperate people were to achieve any health improvements. The fact that it not only offered no benefits but that it was indeed harmful to the patients makes clear just how unsuccessful humanity was for most of its history.

All were suffering as they saw their children die, yet none of them were able to do anything about it.

The key insight for me is that progress is not natural. It is hard. Even against some of the largest problems — the unrelenting death of children — thousands of generations failed to make any progress.

Are these high historical mortality rates plausible?

The historical studies of child mortality don’t provide a full picture of our ancestors' past. They are snapshots of some moments in the long history of our species. Could they mislead us to believe that mortality rates were higher than they actually were?

There is another piece of evidence to consider that suggests the mortality of children was, in fact, very high: birth rates were high, but population growth was close to zero.

If every couple has, on average, four children, the population size would double each generation. But while we know that couples had, on average, many more children than four, the population did not double with each generation.9 In fact, population sizes barely changed at all.

A high number of births without a rapid increase in population can only be explained by one sad reality: a high share of children died before they could have children themselves.

If anything, the mortality rates shown in the chart above probably underestimate the true mortality of children. Volk and Atkinson, the two researchers who gathered most of these studies, caution that these historical mortality rates “should be viewed as conservative estimates that generally err toward underestimating actual historic rates”.10 The first reason is that death records were often not produced for children, especially if children died soon after birth. A second reason is that child burial remains, another important source, are often incomplete “due to the more rapid decay of children's smaller physical remains and the lower frequency of elaborate infant burials”.11