Voldemort's bit in Harry- A horcrux?

The Connection & The Prophecy

We all know that that on the night of Halloween, Big V involuntarily transferred a bit of himself into Harry. But the exact wordings, which I happened to read in COS, said by Dumbledore himself, are quite disturbing. On pg 245, old D, in reply to harry’s questions about how he can speak parseltongue, and which later explained his connection with big V, are…

'...Unless I am very much mistaken, he transferred some of his own powers to you the night he gave you that scar. Not something he intended to do, I am sure...'

'Voldemort put a bit of himself into me?’ Harry said, thunderstruck.

‘It certainly seems so.’

A bit of himself?? It is known that Voldemort lost his body and hence his powers at the time of physical demolition would have transferred to Harry. But ‘a bit of himself?’ A bit of Voldemort’s soul? A Horcrux?

I know that I, in my previous article, openly criticized Harry being Voldemort’s Horcrux theory, but some reading of COS has wavered my mind. Maybe, the Horcrux was made involuntarily. If it is so, it would be fun when big V discovers it. Now, how will he kill Harry? After all, he would not destroy his own Horcrux. Now he would be in difficult situation. Harry would try to kill him, but he cannot fight back as in doing so, he would destroy his own Horcrux.

Harry being big V’s Horcrux explains his parseltoungue, his mind connection with Voldemort, and many other things.

Or maybe, it is just some coincidental writing, from which I am taking out the wrong meaning.

Now I will have to contradict myself, and present the other side of the coin. This theory openly contradicts the Prophecy. The prophecy says- Neither can live while the other survives. If Harry his big V’s Horcrux, one can definitely live while the other survives.

So, the situation is here. Give me your views about what you think may be the possibility, after you have read both the views.