In the electroweak theory, the Higgs mechanism makes the gauge bosons obtain their mass. If the vacuum states of the Higgs fields are the sources of mass for the massive gauge bosons W and Z even electron e-, then this lowest energy v of the Higgs field must be smaller than the Higgs boson of 125 GeV and even the electron’s rest mass 0.511 MeV. Surprisingly, v is equal to 246 GeV revealed in some textbooks. Furthermore, the scalar Higgs boson is charge-zero (q=0) and spin-zero (S=0) so the vacuum states of the Higgs fields have the same characteristics. However, the W and Z bosons are all spin-1 (S=1) and moreover, W bosons are charged. Therefore, how to constitute those massive gauges bosons from the Higgs vacuum states becomes a questionable concept. On the other hand, due to the local gauge invariance, all mass terms are removed and the Yukawa coupling can provide electron’s mass through the Higgs mechanism. How to constitute the electron’s mass and other fermions from the vacuum states is another serious problem. Especially, the electron-positron pair production from two photons directly reveals electron and positron from the photon fields above 1.022 MeV, not from the Higgs field, and no coupling exists between the photon and Higgs fields in the standard model. The mass-energy equivalence shows the mass of particle coming from energy such as high-energy photons, the vacuum states of Higgs fields don’t possess stable energy to support electron with almost infinite lifetime.