Old Major says, more or less, that humans are greedy and they take the fruits of others' labor (without working themselves). They are tyrannical and brutal. I do not think that any of these things are caused by the ability to speak or reason. I think that they are caused by other aspects of being human.
I think that people are able to be selfish before they are able to reason. Babies and little kids (who do not reason) show that to me, at least. I think that a person could easily be tyrannical and greedy without being able to speak.
To me, the thing that leads to the vices that Old Major mentions is power. One way to prove this, in my opinion, is to look at the fact that Boxer and all the other animals can speak and reason but do not fall into these vices. It is only the pigs that "go bad." So why them? I would argue that it is because they have power.
Old Major's stirring speech in Ch. I reveals the vices of human beings. They are:
1. Man is the only creature that consumes without producing: Man according to Old Major is lazy and exploitative and lives off others.
2. The tyranny of human beings: Man is cruel and heartless. After exploiting to the maximum the animals he gets rid of them once they have become useless.
3. Man serves the interests of no creature except himself: Man is selfish and he is not concerned about the well being of the animals whom he exploits.
Nowhere does Major say that these vices are a result of man's ability to speak or reason. But he certainly implies that man has the ability to reason and argue to safeguard his own selfish interests when he remarks,
No argument must lead you astray. Never listen when they tell you that Man and the animals have a common interest, that the prosperity of the one is the prosperity of the others. It is all lies.
So, although Old Major does not state explicitly that man's ability to speak and reason is the reason why man is selfish, exploitative, greedy and tyrannical he certainly hints at and warns his comrades against man's ability to smooth talk the animals into believing and accepting as truth whatever man says.