I've never had a problem with ironing it in half. Is there a problem I don't know about?

Here is a quilt I'm stitching binding on now. You can see front and back binding.
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I always iron the 2-1/4 in binding in half, use a walking foot on a trimed quilt, and use the foot as a guide. I stitch about 5 or 6 inches check to see how it would be on the other side because it matters what batting you use. I also quilt and attach binding for others for a fee, some people use very low loft batting and some high loft poly so you adjust the width of stitch

I fold the corners so that I get a very good miter.

I leave an extra 1/4 batting on also... I do trim it before sewing and then when I sew on the binding I am actually sewing it 1/2 inch from the edge..or 1/4 is the batting and then I sew 1/4 from the edge of the fabric.
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Jenny Doan at Missouri Star Quilt Co has a great tutorial on her site or you can google how to attach binding by Jenny Doan.

THANK YOU everyone for your tips. Each one of you made good suggestions and now I'm anxious to try it again. Thank you!!!

First of all I baste all four sides of the quilt using a walking foot. I cut my binding 2-1/4 inches wide and fold it in half and iron it using a litle "best press". I will cut my batting leaving about an half inch or so all around. Using a walking foot I sew the binding on using a 1/4 inch seam. After it is sewed I check to see how much batting I need to fill in the binding. Cut the remainder off and I'm good to go. Works well for me and fills out the finding nicely.

I do not cut off any extra batting or material on the edge until I have sewn on my binding. That way the binding is guaranteed to have backing and batting in it.

I always trim my quilt leaving a 1/4 inch. This 1/4 inch seems to help in the binding process. If you send your quilt out for quilting make sure that you ask for 1/4 trim otherwise they will trim flush

There are LOTS of techniques for doing binding and it is important that you find what works best for YOU! I do cut my binding 2.25" wide and press in half attaching it using my 1/4" foot. I found a technique that Patrick Lose has used on F&P TV show on PBS has made my corners even sharper. I think that Jenny of MSQC has also evolved to use the technique of sewing off just a 1/4" before you would pivot and sew at a 45 degree angle off to the corner of the quilt. I haven't found it posted on u-tube yet.

Great advice, Pechish! previously I read the suggestion on the board about not 'iron the binding in half' and it works great. My bindings now are so nice that at my last retreat I was doing one and the ladies oohed and ahhed over it. That probably was one of the most important things I have learned from you wonderful quilters.