Is it reasonable?
It is totally reasonable (most of the time) to expect that you should be able to write email in which you take ownership of your work - both the credit and the blame - when dealing with others.
The times when it is unreasonable to expect that universally is when there is substantial risk to the team or organization when the communication does not come from a person of particular authority or talent. Examples:
In a tense inter-team/inter-organization situation - the boss may rightfully want to control the communication wording, because while the work is yours, responsibility for how external groups perceive your team and how well your team's rights and responsibilities are protected - is owned by your boss. When the team's image, rights or privileges are threatened, your boss may want to take ownership of all communication of a particularly heated nature.
In a case of formality, it may be that as the supervisor, your boss MUST do the communication as the legal representative. I've had to to this in cases of contract management, reporting to key customers on contracts, or with HR related situations.
In a case where individual contributors are temporary and/or interchangeable, the boss may be the constant point of contact.
Is it fair in this case?
If your boss can't explain in non-defensive terms (like the ones above) why all email should come through her - then you are probably correct in assessing that the reason is personal - instead of protecting the team, the boss is protecting herself.
This one is harder to fix, since it's a self-esteem issue, and also a defensive situation.
What do to?
It's OK to ask why. You've said you asked indirectly - there's no shame in asking directly. You can even read the emails where she's said defensively that she was going to reply and say that it seems to you like she doesn't trust you to answer emails - is that correct? And why?
She may have a valid reason that fits into my categories above, or similarly business related cases. At that point, you may want to clarify with her when answering emails yourself is OK and when it is her job.
If she can't give you a good reason and manages to dodge around it - you may want to think of some counteractions - because evasiveness can be a strong indicator of defensiveness. Make sure that others in the organization know of the value you contribute to the company - coworkers, adjoining groups, your boss's boss.
In many companies (in my mind, this a must-have) you can also have a "skip level" meeting with your boss's boss. Don't throw the boss under the bus - but if you don't get a satisfactory answer on "why" from the boss, ask the boss' boss. "Hey, I see that is very proactive in sending emails. When I respond before does, it seems that I've done the wrong thing by actively taking ownership and responding. I don't understand why - can you explain?
If there's a good reason, the boss' boss can explain it.
If not, he's on the alert about this behavior.
If he's vague, you can even say - it doesn't make you feel great, it feels like you're not trusted, and no one will tell you why. That's an unsettling place to be.