But why do most people only have about 3% Neanderthal DNA? The DNA of the first human-Neanderthal hybrids was 50% human and 50% Neanderthal. If these hybrids had kids with a human, the percentage of Neanderthal DNA would drop to about 25%. In the next generation, the percentage would be halved again. At some point, the Neanderthals went extinct. We still do not know exactly why. The consequence of this extinction event was that humans could only have kids with other humans. No new Neanderthal DNA could be added to the human genome, and the percentage of Neanderthal DNA diminished to the 3% we see today.
You can compare this scenario to mixing paint of two colors. Let us say you pour yellow (Neanderthal) and red (human) paint in a big bucket. The result is an orange mixture, which represents the first human-Neanderthal hybrid. When you add more red paint, the mix will become more and more red over time. In other words, the DNA becomes more and more human over time, as humans have kids with other humans.

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Go to source: https://kids.frontiersin.org/article/10.3389/frym.2019.00104