There are times when you tire of the same old scales or licks and want to create a different tonality for your solo or lead fills. Symmetrical patterns are useful for creating interesting tonalities, but sometimes sound "unmusical" for certain passages.
One way to ensure your symmetrical scales sound good is to make sure you resolve to the root note of the key you're playing in, or the chord you're playing over. Even when improvising, if you know where the root is, you can create symmetrical scales on the fly, and resolve to the root note.
Another interesting way to create symmetrical scales is to take a fingering you are comfortable with and use it across the fretboard. Then try and "reverse" it by changing one fingering, such as swapping the middle finger with the ring finger.
Experimentation is the key.
The first four scales resolve to the A note:
The next three resolve to E.
Now, for a few variations. The scales start symmetrically, but end with more of a "traditional" scale structure.
Try these scales starting on different notes within the scale. If you're just learning theory, be sure to at least learn where the root notes are for the key you are playing in. Symmetrical scales are a great way to bring contrast to traditional scales.