Why was Flash updated to 10.2? Is a downgrade possible?

The Flash plugin from Adobe is non-free, so it cannot be maintained by Ubuntu developers. Typically, when a new release of software contains important security and stability updates but also major changes in functionality and new (potentially buggy) features, Ubuntu developers create a new Ubuntu-specific version (or multiple new Ubuntu-specific versions, for different supported Ubuntu releases) by backporting (http://en.wikipedia.org/wiki/Backport) the security and stability fixes to the existing versions.

Since Adobe Flash is non-free, this is not possible. Most updates to Adobe Flash contain fixes for security issues. Sometimes Adobe releases updates to multiple major versions of Flash, but the older versions' support from Adobe still expires eventually, and at that point, it is necessary to switch to the latest version to get updates.

Finally, Ubuntu does not actually provide a package containing Adobe Flash through the traditional repositories. Ubuntu provides a package containing an installer (flashplugin-installer), which itself downloads and installs Adobe Flash. This installer is not upgraded to later major versions in the same release, but that doesn't mean the version of Adobe Flash it installs is not upgraded. Ubuntu also provides, through the partner repository (a.k.a. "Canonical Partners"), the package adobe-flashplugin. That is a package for Adobe Flash itself, but packages obtained through the Canonical Partners repository are mostly proprietary software and don't generally follow the usual "no major version upgrade" rule.

It is for those reasons that you see the latest major version of Adobe Flash in all currently supported Ubuntu releases.

It is possible for you to remove Adobe Flash, install an older version, and prevent it from being automatically upgraded. However, you should really not do this, since you would be vulnerable to the security bugs fixed in the later version. Flash bugs are frequently exploited in the wild, not all bugs are platform-specific (such that an exploit intended for Windows wouldn't cause a breach on an Ubuntu system as well). In addition, we should expect to see more exploits specifically targeted at Linux-based hosts as time progresses and the mainstream status of Ubuntu and other Linux-based systems further solidifies.

You should also be aware that flash applets on the web will gradually come to require the later major version of Flash, such that remaining with an older version will eventually break compatibility.

With all that said, if you understand the considerable security risk and you still want to try to downgrade your Adobe Flash installation, I will attempt to help you do so. In that case, please reopen this question, and include the output of the following command, run in the Terminal (Applications > Accessories > Terminal):

dpkg -l | grep flash; dpkg -l | grep gnash; dpkg -l | grep swf