Men and women are equal under the law (in most or all European states) when it comes to labour.

Gender inequality in Europe is largely caused by individual choices. This is best demonstrated by the fact that in poorer countries of eastern Europe, women are much more represented in STEM as it's a good way out of poverty, while richer countries (such as Scandinavian) where women have more choice, the interest gap for STEM is much more skewed in favor of men.

It should also be noted that in countries where a company cannot fire you for going part time at work, it is women who overwhelmingly take advantage of this.

Also, equating the inequality of women in the middle east with Europe in any way is ridiculous.