hubris
Latvia's population has shrunk by 13% in a decade. Working population by 15%. By a strange coincidence, they joined the EU in 2004.
Lithuania's population peaked in 1991 and has been in steady decline ever since. The rate of decline has not changed since joining the EU. The population increased quickly after it was absorbed by the USSR and declined when the USSR collapsed.
en.wikipedia.org/wiki/Demographics_of_Lithuania
If you look at the demographics of Romania, you'll see the same trend.
en.wikipedia.org/wiki/Demographics_of_Romania
In fact, most (if not all) of the former Soviet countries are experiencing the same problem. Even Russia itself underwent a period of post-Soviet population shrinkage, up until very recently.
I'm not saying population loss isn't an issue that needs to be addressed, and I'm sure that the EU could do more (if the rich member states were more willing to help), but we cannot blame the EU for causing or even enabling population loss. For the people living in former Soviet states I'm sure they're mostly happier coming to the EU than Russia, which is the obvious alternative. Seeing the damaging political impact Russia has on nations like Ukraine, I'm sure countries like Romania and Lithuania are happier being in the EU.
I've used Google more in the last few weeks than ever before, trying to get to the bottom of all the claims made by both sides. There has been an awful lot of misunderstanding and misrepresentation.