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According to Lieb's theorem the ferromagnetic interaction in graphene-based materials with bipartite lattice is a result of disbalance between the number of sites available for pz electrons in different sublattices. Here we report on another mechanism of the ferromagnetism in functionalized graphene that is the direct exchange interaction between spin orbitals. By the example of the single-side semihydrogenated (C2H) and semifluorinated (C2F) graphene we show that such a coupling can partially or even fully compensate antiferromagnetic character of indirect exchange interactions reported earlier [Phys. Rev. B 88, 081405(R) (2013)PRBMDO1098-012110.1103/PhysRevB.88.081405]. As a result, C2H is found to be a two-dimensional material with the isotropic ferromagnetic interaction and negligibly small magnetic anisotropy, which prevents the formation of the long-range magnetic order at finite temperature in accordance with the Mermin-Wagner theorem. This gives a rare example of a system where direct exchange interactions play a crucial role in determining a magnetic structure. In turn, C2F is found to be at the threshold of the antiferromagnetic-ferromagnetic instability, which in combination with the Dzyaloshinskii-Moriya interaction can lead to a skyrmion state. © 2016 American Physical Society.