The efficiency of silica supported d(0) ML4 alkene metathesis catalysts [(equivalent to SiO)M(NR1)(=CHR2)(X)] (M = Mo, W; R-1 = aryl and alkyl) is influenced by the nature of the X ancillary ligand. Replacing the alkyl ligand by a pyrrolyl ligand dramatically increases the performance of the catalyst. DFT calculations on the metathesis, the deactivation, and the byproduct formation pathways for the imido Mo and W and the alkylidyne Re complexes give a rational for the role of pyrrolyl ligand. Dissymmetry at the metal center leads to more efficient catalyst even when the difference in sigma-donating ability between X and OSi is not large. beta-H transfer at the square based pyramid metallacyclobutane is the key step for catalyst deactivation and byproduct formation. Overall, the greatest benefit of substituting the ancillary alkyl by a pyrrolyl ligand, [(equivalent to SiO)M(ER1)(=CHR2)(pyrrolyl)], is in fact not to improve the efficiency of the catalytic cycle of alkene metathesis, but to shut down deactivation and byproduct formation pathways. Pyrrolyl ligand, and more generally ligands having metal-bound-atoms more electronegative than carbon, disfavor mostly the two first steps (beta-H transfer at the metallacyclobutane and subsequent insertion of an ethene in the M-H bond) of the deactivation channel. The [(equivalent to SiO)M(ER1)(=CHR2)(pyrrolyl)] catalyst is thus highly efficient because pyrrolyl ligand is optimal: (i) it is still a better electron donor than the siloxy group, thus, favoring the metathesis pathway (dissymmetry at the metal center); and (ii) the nitrogen of the pyrrolyl ligand is more electronegative than the carbon of the alkyl group, thus, specifically disfavoring the decomposition of the metallacyclobutane intermediate via beta-H transfer.