Hello, I have a cok age 105 and level 50 but I can't choose the option breed?! Why, I bought it to breed since a very good cok, but I can't... IS she too old?

Ah yes, and she is full energy.

Link the pet please?

Hmm... Some of your wording is a little confusing, but I think I see what you are saying.

Do you have space in your stable? Has the pet used all her breedings? Does the male have enough energy (and also have breedings left). Is your pet currently busy exploring, crafting, on a quest or on the battlefield? 

Just a few possibilities. Also I am moving this to the help board. ^^

I'm assuming you're talking about Kiwi, since she is the only lvl 50 Cockatrice in your stable that I can find. She is currently exploring an island. While she is on an island, she cannot be bred. You have to have her as acitve pet, click on Explore and then leave the island via the portal. 

I'm pretty sure that will fix the problem. There is no age limit for pets, so she is not too old and she only had one baby so far, so her breeding limit of 25 has not been reached yet either. 

For furture reference, linking a pet that you have a problem with makes it much easier for people to help you, so you should always do that. And secondly, if you want to shorten the name Cockatrice, rather go with Trice. That's the common form for them.