That's a question most people don't ask - good one.
The Higgs boson interacts with itself as well as with other particles. So, the Higgs boson gives itself mass.
The mass "created" by the Higgs boson is manifested as the mass equivalent of the interaction energy between the Higgs and other particles (including itself). When you think about it, it isn't strange for a particle to interact with other particles of the same kind. Electrons repel other electrons, protons repel other protons, etc.
The Higgs boson interacts with itself as well as with other particles. So, the Higgs boson gives itself mass.
The mass "created" by the Higgs boson is manifested as the mass equivalent of the interaction energy between the Higgs and other particles (including itself). When you think about it, it isn't strange for a particle to interact with other particles of the same kind. Electrons repel other electrons, protons repel other protons, etc.