Could you explain in non-specialist language how similarities between these modern languages now has anything to do with their relationship from some earliest common ancestor? How is that explanation better than convergent evolution or overfitting hallucinations?
When I look at the difference between modern and “old English” they seem to have changed quite a bit [0]. When I read an etymological explanation [1], it sounds like a just so story.
English is a bit special in that it's a relatively modern mix of Old English (aka Anglo-Saxon) and what the invading Normans spoke (a Romance language), plus some more. So when you compare words it's maybe better to look at the origins of the modern English words. "Ignite", for example, is from Latin "Ignitus", via the Normans. It's fine to include English when comparing words from different IE languages, but perhaps not as the only "Western" example. Wikipedia has a much broader list which is more interesting: https://en.wikipedia.org/wiki/Indo-European_vocabulary
But it's not as good as I would wish. English is included as the only modern western European language. No German, no Swedish, no Icelandic, no Dutch etc.
The explanation is better if it allows you to explain a large number of similar words arising from a common source by a systematic process.
If you have to make up a new just-so story for every pair of words, of course you're not gaining much, but if the same story works for many words at the same time, positing a common origin isn't too far-fetched.
When I look at the difference between modern and “old English” they seem to have changed quite a bit [0]. When I read an etymological explanation [1], it sounds like a just so story.
0. https://www.reddit.com/r/etymology/comments/9ouweu/how_engli...
1. https://www.pimsleur.com/blog/words-for-father-around-the-wo...