This issue of a developer testing his own code comes up often. I think there is value in it. However, not as much as people make it out to be.
Memes like this mask the bigger issue, i.e., there not being an understanding of testing. Many teams don’t use TDD, test first or BDD. What happens in that case? TDD also is not about test.
This is testing: https://medium.com/@revelutions/how-cem-kaner-tests-software-17e3d6fc6157 . It’s perfectly fine if a developer can test like that. If he does, he may be able to be unbiased about testing his own code.