As a teacher, I always had children tell me "I can't read". Now at 5 many children understand that the reading of words is the actual act of reading, but they don't have to believe they can't read. I always told children that if they can tell the story by the picture that they can read "like a kindergartner".
The other day I asked Colby if he wanted to help me read his book and he told me that he can't read. I went on to show him that he can read. Colby has a lot of books memorized, now yes this is not "reading" but it is a true understanding of book knowledge. If your child can recite books and know what words go on what pages they are on the path to learning to read. They will soon begin to realize that what they are saying matches the text on the page. When I read these books to him (the easier less words ones) I will text match while I'm reading. This is the simple task of pointing to the words while I'm reading.
The next step is to read the first part of the sentence and have your child finish your thought. Most kids will naturally do this on books they have memorized if you stop reading. When your child is reading continue to point to the words as he/she says them. This will help them learn to follow text while reading as well as see that the words they are saying is connected to the text on the page.
Another great way to show children that they can already read it to point out "environmental print" that your child knows how to read. Environmental print is words that your child sees within his/her environment. Can your child read the name of his/her favorite cereal or snack? Does he/she recognize the names of stores you visit often? Can he/she read a stop sign? These are all beginning stages of reading. When I had struggling readers I often made them books of these types of labels so they had at least one story that they could read on their own. When you are done with a box, cut the name off and glue it on sheet of construction paper, you can group words into categories and put the name of the category on the top of the sheet this will introduce yet one more word to their visual vocabulary.
The next time your child tells you that he/she can not read, don't agree with them... prove them wrong!