Can a regression coefficient be explained both ways in logistic regression? In logistic regression, depending on the sign of the coefficient we can say, for example, that when predicting political interest, a coefficient of $1.226$ for following the news indicates that people are more likely to be interested in politics when they are following the news. However, can we say that based on this coefficient, the more people are political interested the more likely they are to follow the news? 
In other words, does it work both ways? 
 A: Unfortunately, it works only non-directionally, as you cannot make causal claims without a proper design that manipulates one of the variables. A regression does allow you to estimate criterion values based on predictor values but it doesgive evidence for a causal account. 
You also have to be caeful with the statement "the more... the more...". A regression coefficient can owe its direction due to a single extreme outlier. 
Therefore, unfortunatley, you do not have the evidence to make either claim as a general or even causal claim.
You can make a descritpitve statement about your sample though after carefully analyzing the data. In that case you cannot restrict directionality to one direction, and both claims are equally valid descriptions. I would still try to avoid causal implications, even though it is very common practice to mix this up...
A: This is essentially a philosphical question, a variation of the chestnut of 'association is not causation'. The answer will depend on context. Ultimately it requires the 'counsels of the wise' in order how to determine how to interpret the association that is illustrated in the model.
Both variables here are binary: Outcome='interest in politics' and predictor='follow news'. This does seem to be something of a simplification. If that's the data you're given then it can't be helped. However it would seem that these would lend themselves better to ordinal scales, which could always be collapsed later to binary categories if needs be (e.g. low no. responses/ small vol. data).
To some extent it depends whether we're in 'hypothesis-generating' or 'hypothesis-testing' mode. Now if the data was collected in order to try to predict the likelihood of 'being interested in politics' then, in the strictest interpretation, the reverse interpretation should not made. An experiment needs to be designed with a hypothesis in mind before any data is collected (particularly in the frequentist perspective). If the data has just 'fallen into ones lap' then a both interpretations are legitimate. Just reverse the model with 'interest in politics' as the predictor. (You're using a model designed to be predictive but descriptive statistics like chi-square might be more relevant if causation has not been established). 
To my mind, this type of question would seem better suited to a qualitative/dialogue-based approach rather than binary scales. It seems plausible that both are signs of something bigger/underlying e.g. 'societal engagement', 'will to power' or more basically 'literacy'.  In this vein, principal components analysis might be of interest. It's an established approach to teasing this out quantitatively when you have other measures available.  
