I have worked both with the TensorFlow C++ API and the TensorFlow Python API. While the TF Python API is basically only a wrapper around the TF C++ API, it adds a lot of things on top, e.g. many higher-level functions you would want to use to define neural networks, etc. If you know PyTorch, think about torch.nn. Most crucially, calculating the gradients, i.e. doing backprop/autograd, was also purely implemented in Python. Even to define the gradient per each operation was done in Python. The C++ core did not know anything about this. (I'm not exactly sure how much this changed with eager mode and gradient tapes though...)

So, that makes implementing training with only the C++ API quite a big task. You first need to define all the gradients, and then implement backprop / autograd.