Turkey has recently undergone a failed coup attempt. They are now implementing a three month emergency period to be sure everything in its country remains stable. They should not be having conventions or lots of visitors from other countries right now. They need the time to think about their own country. The European Human Rights Convention can be postponed or relocated.
Coup attempt left a shaken Turkish government that needs to hold it's borders in check while recovering and dealing with the instigators. This isn't the right time for them to be distracted by the European rights convention activities. The leadership can't afford to be out of the office for a few months while things are put back in their rightful places.
Erdogan is using the attempted coup as an excuse to seize more power for himself, the trend which caused the coup in the first place. If the ERC were to be suspended temporarily, it would be only a matter of time until Erdogan suspends it permanently and uses that to dissolve even more of his opponents.
A recent coup is not a justifiable reason to suspend people's human rights. They need to conduct their investigation and prevent the coup from happening again without violating the rights of people incluing their right to have political opinions that differ from the ones held by the current political leaders.