A well implemented UBI would be funded by a progressive tax system that taxes rich people more heavily that anyone else. If that is the case a rich persons taxes would end up increasing more than the UBI amount. At the same time everyone else's taxes may increase some but the UBI would more than cover the increase. That would lead to a net decrease in inequality.

Social corrections to existing system are superior. Not everyone should get the same. Some people need more, some need less.

A UBI as described above is a social correction. In essence it would redistribute money from those who have plenty of excess money to those who are struggling.

but UBI will not accomplish that.

This is just your opinion. How do you know it won't accomplish that when it has never been implemented at scale?

Social-democratic systems such as Western and northern Europe already have, do, to reasonable extent.

Ultimately a UBI can achieve a similar end result as the social-democratic systems. The key is in making sure it is implemented well. UBI is just a way of achieving the same goal in a different way.