Why are there not two trees of life?
The emergence of life out of matter is a very rare event.
The chance of having such event occurring more than once in a small time-frame is very little.

If the time-frame is large enough, then "New Life" could emerge again. However, in that case, the new emerging living organisms would be extremely disadvantaged by the presence of the "Old Life", already evolved to efficiently compete for energy sources etc.

Any new, barely functional, primordial life form cannot outperform the already existing ones, thus it would undergo extinction pretty soon. And that is why we ended up with a single tree of life on this planet.

Some links for further reading:

http://www.science20.com/stars_planets_life/calculating_odds_life_could_begin_chance

http://www.science20.com/news_releases/the_mathematical_probability_of_life_on_other_earth_like_planets

https://www.sciencedaily.com/releases/2018/01/180108090109.htm

https://www.scientificamerican.com/article/universal-common-ancestor/

https://www.nature.com/articles/nature09014

https://link.springer.com/article/10.1007%2Fs00239-010-9407-2

https://febs.onlinelibrary.wiley.com/doi/abs/10.1016/0014-5793%2896%2900631-X

https://www.sciencedirect.com/science/article/pii/S0022519318300419?via%3Dihub