Birch reduction of anisole
Chemistry is an experimental science supported by computational methods. Qualitative explanations for reaction mechanisms follow as a result. More on that issue later.The mechanism of the Birch reduction has been investigated by Zimmerman and Wang.1 What are the experimental results? The Birch reduction is first order in substrate, electrons and alcohol. Therefore, the rate-limiting step is the protonation of the radical anion 2 of anisole 1. Based on the observation that the dianion of anthracene is more basic than its radical anion, 2 the authors designed an experiment utilizing 2% d1-t-BuOH as the alcohol source. The argument is that the radical anion, which is less basic than the anion, will be more discriminating,3 favoring protonation rather than deuteration (isotope effect). The more basic anion, 4 or 7, which is less discriminating, will give rise to a higher D/H ratio. Employing deuterium NMR, the meta position in 8 was found to have 7-times the amount of deuterium than the ortho-position. Thus, the ortho-position (2a --> 3) is protonated first; mechanism O (ortho) predominates over mechanism M (meta). --continued-- 

Calculations showed that the methoxy ortho-substituted cyclopentadienyl radical is more stable than the meta- and para-isomers (red box). But your request was for a qualitative rationale for preferring radical 3 over 6. Radical 3 has an advantage over radical 6 because radical 3 may be written with the radical on the ipso-carbon, the same radical that would be expected to be generated by auto-oxidation of 5-methoxycyclohexa-1,3-diene. Cross-conjugated radical 6 does not have this option.

1) H. E. Zimmerman and P. A. Wang, J. Am. Chem. Soc., 1993, 115, 2205.; H. E. Zimmerman, Acc. Chem. Res., 2012, 45, 164.
2) V. D. Parker, M. Tilset and O. Hammerich, J. Am. Chem. Soc., 1987, 109, 7905.
3) Consider by analogy that chlorine atoms are less selective than bromine atoms in the radical halogenation of alkanes.