  Magnetism in transition metal compounds is usually considered starting from a
description of isolated ions, as exact as possible, and treating their
(exchange) interaction at a later stage. We show that this standard approach
may break down in many cases, especially in $4d$ and $5d$ compounds. We argue
that there is an important intersite effect -- an orbital-selective formation
of covalent metal-metal bonds, which leads to an "exclusion" of corresponding
electrons from the magnetic subsystem, and thus strongly affects magnetic
properties of the system. This effect is especially prominent for noninteger
electron number, when it results in suppression of the famous double exchange,
the main mechanism of ferromagnetism in transition metal compounds. We study
this novel mechanism analytically and numerically and show that it explains
magnetic properties of not only several $4d-5d$ materials, including
Nb$_2$O$_2$F$_3$ and Ba$_5$AlIr$_2$O$_{11}$, but can also be operative in $3d$
transition metal oxides, e.g. in CrO$_2$ under pressure. We also discuss the
role of spin-orbit coupling on the competition between covalency and magnetism.
Our results demonstrate that strong intersite coupling may invalidate the
standard single-site starting point for considering magnetism, and can lead to
a qualitatively new behaviour.
