A very small parachute pointed the wrong way
Why Do Umbrellas Turn Inside Out?
An umbrella flips because wind curling up its outside lifts it, and its ribs are only built to resist a push from above.
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Step 1 of 5
The ribs only brace one way.
Each rib is held out by a strut that pushes against a downward load. There is nothing pushing the other way, so a lift from beneath the fabric folds the whole frame.
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Step 2 of 5
Wind over a curved dome makes lift.
Air has to speed up to get over the dome, and faster air presses less. The umbrella is being lifted for the same reason a wing is.
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Step 3 of 5
Once a rib passes its hinge, it snaps through.
The frame is stable in two positions, one of them inside out. Push it past halfway and it flips to the other stable shape all by itself.
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Step 4 of 5
Vented umbrellas let the pressure out.
A second smaller canopy with a gap under it lets air escape through the top instead of building lift. It is the same trick a parachute uses at its crown.
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Step 5 of 5
Pointing it into the wind is the real fix.
Held into the wind an umbrella is pushed against its bracing rather than away from it. Held sideways it is a sail, and sails are not meant to be held by one hand.
Umbrella frames have barely changed since the 1850s. Every so-called unbreakable design is the same hinged skeleton with better springs.
The short version
The struts brace against a downward load only, and wind over the curved dome lifts it exactly as it lifts a wing. The frame is stable in two shapes, one of them inside out, so past halfway it snaps through by itself.
Try it yourself
Hold an open umbrella out of a car window at walking pace. It pulls upward, not backward.