As an objective (or subjective). "Being a teacher" vs "to be a teacher". What is the difference between gerund and 'to' + verb root ?
My dream is being a teacher.
My dream is to be a teacher.
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These are possible structures: Gerund is generally used to refer to reality or a fact, but infinitive is used for wishes, possibilities, dreams and abstract ideas.
However, your sentence "My dream is being a teacher" is less common.