Earlier quoted context omitted.
Why doesn't transferring money from you to me make me wealthier? It allows me greater access to goods and services, which seems to me to be almost the definition of greater wealth.
The wealth of a society is a reflection of the quality of the people in the society. 10 million in my hands isn't worth as much as 10 million in the hands of warren buffet.
People who win a fortune by the lottery often lose all their money shortly afterwards, even those people who intend to save and invest it. The reality is that some people are better than others at turning capital into gains through investment. There's definitely luck involved too, but Buffet knows how to buy a business, be its steward, and generate growth, not just for his business but for the economy in which it resides too. Simply investment in diversified mutual funds is not the same thing.
If you pick a typical poor person and give them $10m, they probably won't have the education or discipline even (to know how to) live off investment proceeds, much less grow the amount substantially. (See the outcome of most lottery winners)
That being said, basic income is talking about something different entirely, which is giving a lot of people a little bit of money. I think that could have a positive effect, although for all we know it may be transitive and only lasts as long as the money is being supplied. I think the question is whether the money helps people lift themselves out of poverty, and educate themselves or their children so as to enter the middle or upper class.
I think you could have expressed your first post more clearly -- I assume your point is that transferring wealth from one person to another in a particular society does not make that society as a whole better off. On a micro scale this is correct, but it may in fact make society more wealth if it leads to a more productive population in the long term. But it could just as equally lead to a less productive population. We'll have to see.