How come that in most western countries cooking was considered 'feminine' during the early 20th century - as in 'a woman's place is in the kitchen' - yet professional chefs were mostly men? Has this conttadiction existed through the ages? And why?

All my answers here seem to start out "it's hard to say, but...". So, it's hard to say, but the contradiction hasn't been as blatant in previous centuries, although it's still been there.

Most of the documentary evidence from cooks in the classical and medieval era has been written by men. Sometimes the men were the cooks themselves, and sometimes they were writing down recipes provided by other people - which probably included women. In this case, it's the literacy that provides the bias, not the cookery - through good-sized chunks of history, more men than women have been literate. As far as can be told, though (and the actual gender of cooks is not my area of study), there were more women than men cooking.

However, from the Industrial Revolution onward, and particularly in the Victorian era, the concept of 'separate spheres' began to appear. This was an ideology that held that men should handle the public, external matters like trade, business, and so on, and women should handle the private internal matters like children, cookery, and the home. This was in some ways a codification of attitudes that existed before, but also a sort of set of guidelines, particularly for urban life, for people who hadn't had such divisions before.

And it's not that this was unspoken - there were magazines and books in the Victorian period that were really guides on 'how to be middle class'. The inimitable Mrs. Beeton was one of the foremost of these, and one of the clearest indications of intent here is the line:

Men are now so well served out of doors,—at their clubs, well-ordered taverns, and dining-houses, that in order to compete with the attractions of these places, a mistress must be thoroughly acquainted with the theory and practice of cookery, as well as be perfectly conversant with all the other arts of making and keeping a comfortable home.

So what you're seeing is not a division of cooking, per se, but a division of work in the home from work outside the home.

Sources:

Kathryn Hughes, The Short Life and Long Times of Mrs Beeton, 2006

Robert B. Shoemaker, Gender in English Society 1650-1850: The Emergence of Separate Spheres?

Peter C. D. Brears, Cooking and Dining in Medieval England, 2007