Massive, highly magnetized white dwarfs with fields up to $10^9$ G have been observed and theoretically used for the description of a variety of astrophysical phenomena. Ultramagnetized white dwarfs with uniform interior fields up to $10^{18}$ G, have been recently purported to obey a new maximum mass limit, $M_{rm max}approx 2.58~M_odot$, which largely overcomes the traditional Chandrasekhar value, $M_{rm Ch}approx 1.44~M_odot$. Such a much larger limit would make these astrophysical objects viable candidates for the explanation of the superluminous population of type Ia supernovae. We show that several macro and micro physical aspects such as gravitational, dynamical stability, breaking of spherical symmetry, general relativity, inverse $beta$-decay, and pycnonuclear fusion reactions are of most relevance for the self-consistent description of the structure and assessment of stability of these objects. It is shown in this work that the first family of magnetized white dwarfs indeed satisfy all the criteria of stability, while the ultramagnetized white dwarfs are very unlikely to exist in nature since they violate minimal requests of stability. Therefore, the canonical Chandrasekhar mass limit of white dwarfs has to be still applied.
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