How far is English Germanic? (and other issues)

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   (This is a spinoff from the Saxons and Scythians thread in the Ancient Mesopotamia, Near East and Greater Iran, since it's become all about linguistics and has nothing to do with those areas. So relevant earlier material appears there, although I'm trying to set this up as an independent topic.)

If you look at any standard classification of languages and their development you will, traditionally, see a strictly hierarchical structure, identical to the kind of hierarchical structure you see describing the speciation of living organisms. 
In that picture, languages only differentiate through fission: one group of speakers of a given language develops different pronunciation or grammatical habits from others, with the result that the language group splits into two or more. Hence a tree with twigs at the bottom. English is traditionally one of those twigs (sometimes with twiglets bramching off from it) and it's firmly attached along with other twigs to a branch labelled 'Western Germanic', which in its turn as you go up the tree turns out to be a branch of the group 'Germanic'.
And so on.
It's popular because it fits nicely with things like Grimm's Law and the famous consonantal shifts in Indo-European. 
However It's a model that only allows one form of speciation. And that's OK for the animal world, because by definition species once formed cannot interbreed with other species.
Using it to classify languages however can be very misleading. Rumanian for instance is a twig off the Italic branch and so is French. However French (and Spanish, Portuguese, and even Italian) have heavily simplified grammars and syntax compared to Romanian. That brings it closer to the languages classified as 'West Germanic', in particular to English, though to get from French to English via the tree alone takes the same number of steps as going from Romanian to English, which is kind of silly.
In fact, depending on how you draw the tree, Romanian may end up looking closer to English than French is, which would be ridiculous. 
So something is missing from the diagram, something that would indicate the major similarities that English has to French in grammar, syntax (in particular word order) and vocabulary (not of modern neologisms or post-Renaissance intellectual imports, but basic elements of converse like, for example, 'Please' and 'Excuse me' and 'you' instead of 'thou' paralleling 'vous' instead of 'tu'. Even though English, on balance, is probably more similar to the Germanic group than it is to the Romance group.
And of course it should show the similarities that exist between other languages that don't follow the hierarchical relationship pattern, including relationships between English and the Celtic languages, like the progressive verb tenses and the inverted sentence question ('you were there, weren't you', 'he was driving, wasn't he?). 
To simply say, plumping, that 'English is Germanic' hides these truths and they need to be revealed.
It's interesting that even writers who recognise this will then go on to ignore it and stick with the tree model. For instance in wikipedia at http://en.wikipedia.org/wiki/Language_families_and_languages
the writer says 

The concept of language families is based on the assumption that over time languages gradually diverge into dialects and then into new languages. However, linguistic ancestry is less clear-cut than biological ancestry, because there are extreme cases of languages mixing due to language contact in conquest or trade, whereas biological species normally don't interbreed. In the formation of creole languages and other types of mixed languages, there may be no one ancestor of a given language.

and then goes on to describe how you find the one ancestor of two or more languages. I guess because that's easy and well-worked over, and leads to neat diagrams.
More recently it's because a lot of timeand effort has gone into using numerical taxonomy methods to 'prove' the tree model. This has come relatively late into linguistics compared to biology and economics (where I did my research into it). But the 'scientific' authority numerical taxonomy lends to conclusions overlooks, as in other fields has been discovered before, that it depends entirely on subjective choices of elements like the data to analyse and the clustering methods to be used (co-ordinates, metrics).
As an example take http://linguistics.berkeley.edu/~kjohnson/quantitative/historical/historical.pdf and go to pages 180-181, where clustering is exemplified for a number of I-E languages based on lexical similarity. The author happily points out that "With this list of words we can calculate the similarity of Spanish, Portuguese, French and Italian as 100% because all five of the words are cognates with each other in these languages" but manages NOT to point out that, if you look at English, only two of the words are cognate to any other I-E language, none to German itself, one to Dutch and Swedish, and the last to the Romance group.
Of course this is a very simplified basic example of the technique. On a larger scale things would be different. But the principle would remain: an awful lot depends on the words you choose, and what grammatical and syntactical and other elements you include. (And how you use the numerical data to calculate distance between languages and already calculated families.)
A couple of other wikipedia notes:
http://en.wikipedia.org/wiki/Comparative_method#Problems_with_the_Tree_Model
http://en.wikipedia.org/wiki/Johannes_Schmidt_%28linguist%29
And an example of someone's attempt to portray cross linkages, from http://www.cs.utexas.edu/users/tandy/nanterre-talk.ppt#3