Theists: What is the most compelling argument you have heard for Atheism?

[masterofpuppets]

You can get a brief overview here: https://en.wikipedia.org/wiki/Fine-tuned...e#Examples

• N, the ratio of the strength of electromagnetism to the strength of gravity for a pair of protons, is approximately 1036. According to Rees, if it were significantly smaller, only a small and short-lived universe could exist.[12]
  
  
• Epsilon (ε), a measure of the nuclear efficiency of fusion from hydrogen to helium, is 0.007: when four nucleons fuse into helium, 0.007 (0.7%) of their mass is converted to energy. The value of ε is in part determined by the strength of the strong nuclear force.[13] If ε were 0.006, only hydrogen could exist, and complex chemistry would be impossible. According to Rees, if it were above 0.008, no hydrogen would exist, as all the hydrogen would have been fused shortly after the big bang. Other physicists disagree, calculating that substantial hydrogen remains as long as the strong force coupling constant increases by less than about 50%.[10][12]
  
  
• Omega (Ω), commonly known as the density parameter, is the relative importance of gravity and expansion energy in the Universe. It is the ratio of the mass density of the Universe to the "critical density" and is approximately 1. If gravity were too strong compared with dark energy and the initial metric expansion, the universe would have collapsed before life could have evolved. On the other side, if gravity were too weak, no stars would have formed.[12][14]
  
  
• Lambda (λ), commonly known as the cosmological constant, describes the ratio of the density of dark energy to the critical energy density of the universe, given certain reasonable assumptions such as positing that dark energy density is a constant. In terms of Planck units, and as a natural dimensionless value, the cosmological constant, λ, is on the order of 10−122.[15] This is so small that it has no significant effect on cosmic structures that are smaller than a billion light-years across. If the cosmological constant were not extremely small, stars and other astronomical structures would not be able to form.[12]
  
  
• Q, the ratio of the gravitational energy required to pull a large galaxy apart to the energy equivalent of its mass, is around 10−5. If it is too small, no stars can form. If it is too large, no stars can survive because the universe is too violent, according to Rees.[12]
  
  
• D, the number of spatial dimensions in spacetime, is 3. Rees claims that life could not exist if there were 2 or 4 dimensions of spacetime nor if any other than 1 time dimension existed in spacetime.[12]
  

Carbon and oxygen[edit]
Further information: Triple-alpha process § Improbability and fine-tuning
An older example is the Hoyle state, the third-lowest energy state of the carbon-12 nucleus, with an energy of 7.656 MeV above the ground level. According to one calculation, if the state's energy were lower than 7.3 or greater than 7.9 MeV, insufficient carbon would exist to support life; furthermore, to explain the universe's abundance of carbon, the Hoyle state must be further tuned to a value between 7.596 and 7.716 MeV. A similar calculation, focusing on the underlying fundamental constants that give rise to various energy levels, concludes that the strong force must be tuned to a precision of at least 0.5%, and the electromagnetic force to a precision of at least 4%, to prevent either carbon production or oxygen production from dropping significantly.[16]

Regarding your question about why so fragile. Life is extremely complex in its requirements. It is not clear why we should expect the right combination of elements, heat, gravity, radiation, and self-contained planetary feedback loops to be a common occurrence.

Even if the allowable ranges of the values of constants that lead to a universe with structure (atoms, stars etc.) is very small, the fact that these constants need to have very specific values does not make it unlikely for them to have these values. You are ascribing a low probability to the universe having its specific constants without justification. It may be that certain values of constants are more likely than others. Or, what if the range of possible constants for all possible universes is quite small to begin with? It's not necessarily true that the constants can range from minus to plus infinity.

The fine-tuning argument fails on the basis that it cannot establish the purported low probability of the universe acquiring its constants. For all we know the probability could be 1.