Clydey.. I were to parade the street where I live naked, or buy a gun, or poison my neighbour's dog, or laugh at a homeless person - none of which I would do (but could) - doesn't this mean I have some degree of free will?
As far as I am aware, none these thoughts/actions are inherent to my genetic makeup - but I can vehemently confirm this had no part in my environmental makeup.
It's not just genetics. It's also your experiences i.e. your environment. Your biology and your environment shape who you are. Therefore, everything you do is a product of those factors.
If I ask you to choose a colour, one will pop into your head. Let's say you chose pink. Why didn't you choose blue instead? Your reasoning, whatever it is, will be irrelevant. The colour pink just popped into consciousness when I asked that question. Can you really say that you consciously chose it?
Let's take one of the examples you gave. The factors that lead you to poison your neighbours dog are, again, your biology and your environment. There is no aspect of you that you are responsible for creating. Even if you believe that you have a soul, you didn't choose your soul either.