Never link to Wikipedia from your website.
This is a fair thing to ask of people. The explanation is flawed and the advise is a little too firm but in general it is not bad.
If you are referencing a general topic linking to Wikipedia is fine.
If you are referencing a specific thing you should link to the source material rather than a general article. Chances are reasonably good that if your source material is well researched you could get it added to the sources in the Wikipedia article and maybe even update the general article too.
Wikipedia has rules around editing that ensure factually correct information makes it through. Editing can be challenging but if you adhere to these editing can be quite rewarding.