Sometimes our identity and career choice is influenced more by how others see gender than how we personally see gender. Our career choices may have early influence by teachers, family, and other authority figures. The opinions these people have on gender may influence how they direct children in their care.
Gender is a social construct. We see ourselves in the mirror of gender based on what we were taught, how we were treated and what we saw in the adults around us of both the same and opposite gender. As children we are each socialized in a very unique way to associate certain characteristics, activities, and careers with specific genders. Even young children when learning colors often associate certain colors as "boy colors" or "girl colors".
There are two influences in how you see your gender and how it affects your choices: the societal influences and personal influences. Society constructs gender roles, but they are different during differnt eras and also geographical locations. In addition, as I mentioned above, each child is socialized into their definitions of gender by their individual influences and experiences. I believe that our individual experiences are much more effective and lasting in our view gender that the greater overall societal view.
I do not think that our gender itself affects our choices. Instead, it is the way that we have been socialized to see our gender. Different people are socialized in different ways and therefore different people have different views of what careers are appropriate.
For a long time, certain careers were only available to one gender or the other. Although that has changed, there are still careers that we tend to think of as more male or female; while this is primarily subconscious, it probably affects career choice a great deal.
Many of our career concepts are formed when we are quite young; a child who has not had the opportunity to meet a wide variety of people may develop narrow ideas about which careers "belong to" which genders. For instance, a child who has had only female teachers may think of teaching as a woman's job.
Many children are encouraged to act in ways that the adults around them think are gender-appropriate. For instance, girls may be encouraged to dress up and be less active physically, while boys are sometimes encouraged to hide fear or pain and act strong. This can lead to ideas about how one "should" act, which then translate to gender-biased ideas about careers. A woman who was taught to wear frilly clothes and keep them clean may avoid physical careers where she will get dirty. A man who was taught to hide his emotions may look upon careers in counseling or caregiving as inapproprate for males.