By this stage, your little munchkin may start assisting you in undressing herself like pulling off elastic waist pants, socks, velcro attached booties and all. The most common of these is pulling off the socks as these are easy to reach and pull out.
What you need to know
It can be due to any reason like the fabric might be causing irritation, discomfort because fitting is not proper, color and pattern are just too attractive wooing her to play with them or simply just like that. She doesn't want them on her feet. But there are times when you just can't let her without socks as it protect her feet from possible dirt and keep them warm during cold as well.
What can you do
For this you can try certain things like footie stockings that go upto the waist. While going out one can put on lace or buckled booties or footwear that are not easy for them to remove. At night footie pyjamas can be another option. You can also try Skiders traction shoe which have shoe like sole attached with the socks which may give a look and feel of shoes worn to your toddler.
You should also observe things like the fabric of the socks is comfortable or not. Also check if the socks are too warm for her causing sweating and irritation. Always buy proper fitting socks with skin friendly fabric.