Fat is considerably bulkier than muscle (check www.dailyspark.com/blog.asp?post=quiz_how_
for a great photo of this).
It is also pretty difficult to add a lot of muscle mass while running a calorie deficit to lose weight, as the body tends to burn protein for energy rather than creating new muscle tissue.
If you want to reduce the size of your arms, focus on reducing yuor overall body fat through a combination of cardio, all-body strength training and watching your intake, and some of it will naturally come off the arms. While watching your intake is definitely the biggest contributor to fat loss, there is a fair bit of evidence that strength training is more effective than cardio in terms of fat loss.
And yes, you should be strength training for the rest of your life. Not just because of your arms, but because of all the other benefits of strength training - including keeping the weight off longer term, functional fitness (eg. being able to lift common household objects easily) and reducing your long term risk of osteoporosis.