It is possible to know God personally...
The Bible says man's sins have separated him from God...
"But your iniquities have separated you from your God; your sins have hidden his face from you, so that he will not hear." (Isaiah 59:2)
"for all have sinned and fall short of the glory of God." (Romans 3:23)
God created us to know and love Him. But man chose to go his own way and that relationship with God was broken. (Romans 1:19-21) This attitude and its results are what the Bible calls sin.
This separation caused by sin creates some severe problems.