According to frequentists, why can't probabilistic statements be made about population paramemters? I recently read Wikipedia's entry on Confidence Intervals:
https://en.wikipedia.org/wiki/Confidence_interval
There are a few statements that I have trouble understanding:

The confidence interval can be expressed in terms of samples (or repeated samples): "Were this procedure to be repeated on multiple samples, the calculated confidence interval (which would differ for each sample) would encompass the true population parameter 90% of the time."[1] Note that this does not refer to repeated measurement of the same sample, but repeated sampling.

And:

The confidence interval can be expressed in terms of a single sample: "There is a 90% probability that the calculated confidence interval from some future experiment encompasses the true value of the population parameter." Note this is a probability statement about the confidence interval, not the population parameter.

And:

A 95% confidence interval does not mean that for a given realised interval calculated from sample data there is a 95% probability the population parameter lies within the interval, nor that there is a 95% probability that the interval covers the population parameter.[11] Once an experiment is done and an interval calculated, this interval either covers the parameter value or it does not; it is no longer a matter of probability.

I realize that according to frequentist methods, the value of the parameter is, as the quotes above indicate, a fixed value and not a random variable.  It is the sample data that is random.
I also know that often in the "real world", systems that are deterministic can be modeled as probabilistic if there is not enough information about the system itself.  An example of this would be the tossing of a coin.  How the coin lands is a deterministic process.  It is only because there are so many variables that we model it is a probabilistic system.  In other words, in this case, we "paper over" our ignorance of the details of the system with a probabilistic model.
I realize that in a population with an unknown parameter, according to frequentist methods, this value is not a random variable.  Yet, we also know that if we calculate a confidence interval in a certain way, we produce an interval that encompasses the true population parameter 90% of the time.  So then why can't we paper over our ignorance of the value and say "There is a 90% probability the population parameter lies within this interval"?  After all, as we just said, 90% of the time we calculate a confidence interval, the true population parameter  will lie within the interval.  
So even though the population parameter is not a random variable, since we don't know what it is, why can't we make a probabilistic statement about it?
 A: Suppose that you want to model the random behaviour of a certain population. Then you have to associate to the population a density function $f$ (that is, you choose a "normal distribution", "exponential distribution", etc.), and a parametre $\theta$ (that is, if for example your density is a normal, then $\theta$ can be the population mean or the variance, etc.). 
Suppose that you have decided which $f$ you want, that is, the distribution for your population. The goal now is to estimate $\theta$. In frequentist statistics, $\theta$ is an unknown contant to be discovered. That is why we speak about confidence and not about probability.
Example: imagine I want to model the height of the people in England. I associate to it the normal distribution, so $f$ is the density function of a normal. Now I want to estimate $\mu=\text{population mean}$. One takes a sample $X_1,\ldots,X_n$ of heights and uses the fact that
$$ \frac{\bar{X_n}-\mu}{s_n/\sqrt{n}}\sim t_{n-1}. $$
One computes $a$ and $b$ so that
$$ P\left(a<\frac{\bar{X_n}-\mu}{s_n/\sqrt{n}}<b\right)=0.95, $$
that is,
$$ P\left(\bar{X_n}-a\cdot s_n/\sqrt{n}<\mu<\bar{X_n}-b\cdot s_n/\sqrt{n}\right)=0.95. $$
Here it makes sense to speak about probability because $\bar{X_n}$ is a random variable. Now, what you do is to substitute $\bar{X_n}$ (random variable) by the sample mean $\bar{x_n}$ (constant value), and your confidence interval is 
$$ I=[\bar{x_n}-a\cdot s_n/\sqrt{n},\bar{x_n}+b\cdot s_n/\sqrt{n}]. $$
The parametre $\mu$ is a constant, so either it belongs to $I$ or not (you do not have probability here). But you have a lot of confidence that it will belong to $I$.
Remark: opposite to frequentist statistics, one may use bayesian statistics, which assumes that the parametre $\theta$ is a random variable, with a probability distribution to be discovered. In this case one speaks about credible regions (probabilities) and not confidence intervals (confidence).
