What is it called when there is weakness and bendyness in elbows when performing pushups?

Hypermobility: If you can straighten your elbow and then bend it more, you have a hypermobility syndrome - which is usually without other effects. Sometimes it can be caused by hereditary conditions such as ehlers-danlos syndrome or Marfan syndrome. Someone with "bendy elbows" that hurt should see a doctor for evaluation. (internist or rheumatologist).