The book which I like is on the table.
Can we leave out which in this sentence?
The book I like is on the table.
Why can we? Is the book not the subject of the sentence?
I is the subject of this sentence , the book is direct object
If we ask what is on the table? I?
'book' is the subject.
Volcano, you are asking why we can delete "that". Why not tell us why you think we can't.
"The book that I like ..." > "The book I like ... " is probably one of the simplest cases of leaving out the relative pronoun (that) I can think of.
In simple sentences such as this the relative pronoun can be left out Brevity is increasingly preferred in modern English owing to paucity of space and reader time but not at the cost of confusion of the meaning intended