Not all students studying law can become lawyers.

Literal

Law [object-を] studying students [subject-が] all lawyers [into-に] become-[potential-なれる] [quotative-という] [sense-わけではない]

~というわけではない is a pattern for partial negation: 'it's not that all X...', 'it doesn't necessarily mean that X'. 法律家 literally 'law-expert' is the broad term covering lawyers, judges, prosecutors — the professional class of law. なれる is the potential of なる ('to be able to become').