Why do you need a common ancestor when merging Git?

For example, suppose you changed the file hoge.txt to two branches, respectively:

hoge.txt

A
hoge
B
C

hoge.txt

A
B
piyo
C

Try merging these two.Can you do it?

Which of the following merge results should I choose?

• Right to include both hoge and piyo which were not originally present
• "Deleted hoge and piyo respectively" is correct not to include either
• "Actually, branchA has not changed anything" branchB is correct
• "Actually, branchB has not changed anything" branchA is correct
• What about B that was added in both B was not even there
in the first place?
• etc...

To determine this, you need the information How did each change to a common ancestor