The real reason the American Bear Flaggers put the Grizzly on the flag was to send a clear message to Mexico. California was a part of Mexico in 1846. It was the Mexican / Californio Rancho owners who despised the grizzly who came out of the hills to kill their cattle. It was more of an "in your face" message to Mexico. The grizzly bear does not climb trees or back up, it only goes forward.
The American settlers who endured so many hardship in their wagons moving west, were afraid the Mexican government was going to expel them from California (because the Mexicans feared all of the settlers coming west on wagon trains would stay and change the culture of California.)
The Americans wanted to send a clear message to Mexico that after going through so much to reach California, they were NOT going to turn back - but they would continue to move forward like the grizzly. Just imagine the Donner Party survivors having any intention of going back after all they endured.
Very interesting to compare and contrast what went on in California in 1846 and today.