The problem is that the original file is lying to you about it’s actual filetype! 
I just downloaded it, and although it has a .jpg suffix, the file contents are different:
$ file ~/Downloads/sydtra_r140964636590635_599_big.jpg
/Users/apiper/Downloads/sydtra_r140964636590635_599_big.jpg: PC bitmap, Windows 3.x format, 607 x 330 x 32
To use this on Twitter, you’ll need to convert it into an actual JPG format before uploading. It is likely that when you do the resizing and save it as JPG, that conversion is happening, so that’s why you don’t get the error when you do that.