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In short, child bearing and breast feeding are both associated with a statistical reduction in the relative risk of the development of breast cancer.
Statistics apply to populations, individuals may have different experiences based on their genetics and other factors.
Answers based on individual experience, are just that. Individual experience and not rigorous statistical analysis.

It is correct that breast cancer arises from cellular mutations. However, the reason why having children at a younger age decreases the lifetime risk of breast cancer is due to the changes in hormones that comes with pregnancy. In short, estrogen induces growth of breast tissue, and the cyclical rise and fall of estrogen can induce mutations in breast tissue. Pregnancy changes estrogen levels to be more constant, and it is thought that this provides the protection against breast cancer.

It is important to recognize, however, that having a child at a young age does not reduce the risk of breast cancer to zero; nor does having no children increase the risk of breast cancer to 100%. These risk factors may have very little noticeable effect on subjective personal experience (as you say, people who have children young may still get breast cancer, and people who never have children may never get breast cancer), but if an oncologist or primary care physician were to look at their records and compare breast cancer rates versus age at first birth, they would find that a greater percentage of women who had a late birth or who never had children have had breast cancer.

It is also important to recognize that no physician would recommend having children at a younger age simply to reduce the risk of breast cancer. The most important risk factor that people *can* change is smoking. If more people were to stop smoking, we could reduce rates of breast cancer, and many other types of cancer.

I hope this helps.