My husband had no problem with me nursing past one year, but around the 2.5 year mark he started getting a tad uncomfortable & we had to have some conversations! All I can suggest is that this is different from when a stranger or even another family member objects or questions your choices. As the co-parent who is (hopefully) equally invested in the overall health and wellness of your child, dad deserves the respect to have his concerns listened to and talked over. Conversely, he will hopefully give mom the respect to listen to her views. And also to consider things from the child's point of view, which can usually be inferred if not articulated.
We have to remember that, unfortunately, due to widespread formula feeding and other factors, in many parts of the world, nursing past a year, or even past 3 months(!) is not the norm. Or rather I should say, is no longer the norm, as, prior to formula, it was the norm in many cultures. (And of course still is in some.) We learn about parenting from not only our own parents but from our peers, from the media, from what we see around us. And in many parts of the world, we have been a formula feeding culture for several generations and that has taken its toll on not only how we feed our children but how we view our children, not to mention, how we view breasts!
So I think your husband's concerns, (whatever they are) while, in my opinion, are likely scientifically unfounded, are also certainly understandable given that, just like all of us, he lives in a culture that generally views breasts as primarily sexual organs, a culture that is thus uncomfortable with breastfeeding in general, and a culture that is particularly dismissive if not hostile, and frankly, a bit weird, about nursing past the age a child can walk (or talk, or "ask for it" or whatever the supposed deadline is.)
Also many dads have more personal concerns about it-perhaps they feel that mom nursing the child is interfering with the couple’s ability to be intimate. It would really help to know specifically what his concerns are so you can address those respectfully.
I know that for moms nursing into toddlerhood, having a community of moms who are also nursing that long & can hold up a positive mirror of the experience for each other makes a big difference in their feeling empowered to go against the tide. So I would suggest looking around for some type of parenting group you both could attend that has a positive attitude toward extended -I mean, normal length nursing. Maybe you have a local LLL group with a couples meeting, or an Attachment Parenting International Group?
If you are like most other couples this will not be the last time you disagree on a parenting issue. It can be so very difficult to talk about these things calmly where emotions are high. So learning how to listen to each other and discuss the issues with mutual respect and kindness, and also to know when something is important enough to you that you will make a stand, and when you will compromise, will serve you and your children well.