Synthetic clothes (ie manmade fibres like polyester) are mostly made of plastic which is really really bad for your skin and your hair, especially if you have eczema.
Non-synthetic clothes pack more bang for their buck when it comes to protecting you from the weather - a thin wool jumper does so much more than a bulky polyester one, a cotton top will let your sweat out which is so much better for both summer and winter, and so on.
Synthetic materials are often used because they are cheap so it serves as a good (but heavy handed) litmus test about the quality of garment, because if they've cheaped out on the material they have probably cheaped out elsewhere in the process.
Fire resistance - I wore a synthetic dress near a fire recently and as embers fell on me it literally just melted holes into it.
If you're interested do what I did - find all the cotton, linen and silk in your wardrobe and priortise wearing those clothes for a month. Then you will start noticing the synthetic clothes feel uncomfortable. Wool is also non-synthetic but a lot of people find it difficult to tolerate. Don't forget it's not just clothes, it's bedsheets too