Unable to attach file - file size too large (Samsung S3 - AT&T)

Not satisfied with having to upload to YouTube and/or Dropbox or record video with major sub quality MMS limits, in order to send a simple 30 second video.
Problem- video-too large to send.
Example-iPhone 5 on ATT network can send example.
Lesser quality Android on TMobile can send example but you are telling me that I can't on my Samsung Galaxy 3S on AT&T? I just don't get it based on my two example above and beyond disappointed.
Any new APP that will allow conversion keeping the original quality and sending a sub quality 30-40 second video?

Thank you
Pat / Boston

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