I don’t think either of you are being entirely unreasonable. It’s hard to say from what you’ve said who is most reasonable.
In one hand, it is not unreasonable to want to retrain if you have found something you really want to do. Enjoying your job, if at all possible, is important. And if that job comes with a good wage and security, it could be a good investment too- benefitting the whole family. A partner should want their spouse to be happy in their career and support them in their ambitions, when possible.
On the other hand, you and your DH had made financial decisions together- I.e. to save for a house. All of a sudden (from his perspective) you’ve thrown it all up in the air. I honestly think if you are expecting someone else to support you financially, and in addition you have other financial commitments (E.g. a child), then that has to be a joint decision, not a unilateral one.
I don’t think it’s unreasonable of your DH to baulk a little at suddenly becoming the sole financial provider- and I imagine will have to take up a large proportion of childcare as you progress through the course and need to work shifts. I’m not saying he cannot he asked to do this, merely that he will be shouldering all of the financial responsibility and a high proportion of childcare for the period of your study. As it will impact on him, you have to take his thoughts into account and try to come to a joint decision.
The other thing is- did you just sprung this on him? If he had no inkling you wanted to be a nurse it might appear to be a bit of a whim- even if it isn’t from your perspective. In his position I’d want to be sure you’d thought it through. I would expect you to come with a plan- it will take x long, I will probably be entitled to y support (or tell me that there is nursing if that is the case), prospects are z. If my partner said “ I’ve decided to retrain, so we’re not saving any more” with no plans, no idea of what support is available, not even thought about how we might cope with the loss of their income in the here and now, then I think I’d be a bit unenthusiastic too. Maybe you have gone to him with facts and a plan, it’s not clear from your post.
Frankly, I don’t agree with one poster saying as OP has given birth to his child he should be so grateful that he does whatever she wants. I assume having the child was a joint decision and something OP also wanted.
In summary, you’re not unreasonable to ask and he would be unreasonable to give a flat “no” without sitting down and talking it through. But you would be unreasonable not to consider his concerns too.