You're right not forcing the issue. But this is something that merits at least a dialogue. You don't have the right to force your partner to do what you want on this, but you have the right to be able to speak about your desires, and having them acknowledged.

Forget about this idea of burden, this is not for you to decide, and if you are serious about that, you should be clear about sharing the workload. And yes, there are also the specific burdens of pregnancy, lactation that you can't share, but also for plenty of women, there is also a reward for those activities. A reward that you as a man can also only reap vicariously. So, for every woman there will be a different balance of perspectives, some value more the rewards and will be happy having kids, others will feel more actually the burdens. Not your business to decide that.

But, what is your business is to understand what is important to you. To understand that if you feel so strongly about it now, it probably won't go away and that you will resent over time, if not right now.

And then, if you have such different attitudes about this matter, maybe, just maybe, it would be best for both of you to free yourselves from each other.