There used to be a joke in the old USSR that Estonia was the biggest nation on earth because it's coast was on the Baltic, its capital in Moscow and its population in Siberia. The country lost its independence during World War Two when it was annexed by the Soviet Union so understandably they aren't particularly happy with the Red Army and are keen to remove traces of its legacy like great big Red Army shrines in the middle of their capital. Given that Estonian hostility to the USSR stems from the destruction of their independence the behaviour of Russia has been undiplomatic at best, with senior Russian figures declaring that it not a domestic affair of Estonia. Russian nationalists still feel that the former USSR and Eastern Bloc is part of some mythical sphere of influence which entitles them to over rule the democratic wishes of their neighbours. This is a feeling that is clearly being stoked by Putin and his supporter to bolster his domestic appeal.
What makes it even more insulting is Russia's risible claims that the Red Army were an anti fascist force who liberated Europe and that dismantling their monuments is therefore pro Nazi. In fact the annexation of Estonia was part of the Nazi Soviet pact originally, so the chutzpah is breathtaking.