<p>^Am I missing something?</p>
<p>The 25th-percentile gives you the “75% over and 25% under” point you want.</p>
<p>The 75th-percentile gives you an <em>additional</em> information - 25% over and 75% under. Are you complaining that they give too much information? 
</p>
<p>By the way, the middle 50% is a very common range to be used in statistics (interquartile range).</p>