Poverty and income inequality are complex issues and a wide range of approaches to these problems have led to the development of many different social and economic programs. UBI could replace many of those programs, for better or for worse.
UBI is essentially a generalized welfare program, and it would inevitably supplant existing welfare programs, which are more specialized. Specialized welfare programs can target wealth transfers to the people most in need, such as those experiencing unemployment, undergoing housing problems, or living with disabilities. In contrast, UBI would transfer wealth to everyone equally, resulting in a relative benefit for the wealthier members of society, who are not eligible for specialized programs for the needy, but would receive UBI payments in spite of their lack of financial need. Therefore, rather than fighting poverty, UBI would lead to greater income inequality. The money that is given to those who would not be eligible under a traditional welfare program is lost and cannot be put to use for those who would really benefit from it. 
UBI does not increase inequality as it is an important factor in reducing them. It gives everyone a minimum level of financial assurance that will allow to redirect efforts in a more productive way.  UBI will not make inequality disappear but it will not increase it either. UBI will be just a basis that goes beyond the amount of social welfare most people in need receive and will thus give them access to more resources. UBI will not make specialised social welfare disappear. Special needs like disability pensions etc. will still be intact and added to UBI. 
More money for everyone does not make inequalities disappear.
[P1] Targeted welfare programs transfer wealth disproportionately to those who need it most. [P2] UBI would transfer wealth to everyone, regardless of need, resulting in a comparative benefit for the rich.
Rejecting the premises
[P1] UBI is better in targeting those who need it most than welfare programs. [P2] UBI would transfer wealth to everyone, regardless of need, resulting in a comparative benefit for the poor.