I think that Biden himself -- if he didn't have to think about anything other than his own personal preference (and limiting it only to women, which he vowed in the last debate) -- would probably choose someone like Amy Klobuchar who (as this Politico article notes) "has the governing experience and ideological profile to mesh well with Biden." She has experience, has been vetted by the media and the opposition due to having run for President herself (where she did surprisingly well, coming in third place in New Hampshire) and is not too old or too young (today is actually her birthday; she just turned 60). However many progressives are unexcited by the prospect of someone who will "mesh well with Biden" and he needs an enthusiastic Democratic base in November in order to compete effectively with the raw, unashamed enthusiasm of Trump's voters.
Elizabeth Warren is the best known of the choices and might cause women and progressives to be more excited about voting for Biden, but on the other hand Biden might be afraid that the Republicans could tar her as being "a socialist" who is going to have the government take over every aspect of a person's life. I think Biden wants to peel off some disaffected Republicans from Trump, and having Warren as VP might prevent them from voting for Biden. Another drawback is her age: she turns 71 next month (June 22); still younger than Trump (who turns 74 next month) and Biden (77) but older than Mike Pence (who turns 61 next month). In the entire history of the United States, every person was under the age of 70 when they became Vice-President, with the sole exception of Harry Truman's Vice-President Alben W. Barkley who became VP when he was 71 years old in 1949. (He died of a heart attack while giving a speech in 1956.)
I like Stacey Abrams because she is young (46), African-American and isn't currently tied down with a job somewhere else (Senate, Governor, etc.). But some people might say that she lacks the experience needed for a VP of the oldest President ever elected (if Biden wins). Obama was a young (47), untested candidate in 2018 and so he chose a member of the old guard (Biden, who was 66 years old at the time) to give some comfort to people who thought he wasn't ready. Likewise Trump chose Mike Pence who was trusted among the Republicans as a reliable rock-solid Republican and not an unpredictable loose cannon like himself. Biden needs to choose someone who could step into the Presidency if something happens to him, so that people who say "he's too old" would at least feel that the country is in safe hands if he can't finish his term due to health reasons.
Gretchen Whitmer also has youth (48), but experience as well, being a sitting Governor of a swing state. However, a lot of Republicans have already been criticizing her for shutting down the state (even among people who don't live there, whipped up by Trump), so like Warren she is unlikely to appeal to many disaffected Republicans or libertarian-minded independents.
That leaves Kamala Harris (at least among the choices listed above). She is young (55), black, and also has experience -- not only in the Senate, but also having run for President and generally performed well in the debates. She can point to her time as California's Attorney General to show that she is big on "law & order" which might help to attract some Republicans. So looking at all of the above, that's why I think Biden is now more likely to choose Harris than the others.
We'll find out for sure in July or August, though!
