The problem is the mental construct of "I". Yes we can't help but believe that there is feeling, thinking, subjective experience etc. The problem is that our brain seems to naturally construct a concept of "I" which is a sort of owner of these subjective experiences that persists over time. This construct, while deeply engrained and probably useful, is not consistent with physical reality. This can be seen either with teleporter type thought experiments or to some extent with real life cases of brain trauma (for example in Oliver Sacks's or Ramachandran's books). Our brains' care about protecting some potential future entities, which barring crazy technology or anthropic scenarios are easy to specify, but there is not going to be a coherent general principle to decide when we should count potential future entities as being us.