I just checked the older version and basic HTML to be sure, and the opsiotn to add CC or BCC is there in every version, even if you start composing a message from your Contacts screen. In Basic HTML it is right ther and highly visible, so that is most likely not how you are viewing Gmail. In the other versions, there is a link to click on to add a space to type in contacts.
Part of the problem is that you are searching for a contact and selecting them to compose to. In other email services that might be the easiest way to do it, but Gmail has an easier way. Just click on the "Compose" button on the main screen, and start typing in part of the name or nickname or email address of whomever you want to send the email to. Gmail will opo up a list of possible matches form your contacts list, and as you type, it will narrow down the list. You can select one from the lst at any point.
For example, supose you want to send an email to "Robert Burns" <
bobbi...@nowhere.net> . Type in "bur" or "rob" or "bob" and he will rise to the top of the pop-ups (depending on how many other Robert's or Burns's or similar stuff you have in your contacts).