When we go to study a language, most of us look at it as a fixed entity, stuck in the present time. Where the language came from doesn't matter, because we want to be able to speak it as it is spoken now. But ignoring the history of language and language evolution often causes problems and wastes time. Knowing the history of a language — even a few basics — will often help explain many of the anomalies of how a language works.
Whatever language you're learning, irregularities in a language can only persist in the most commonly used elements. English is a prime example. Think of "irregularities" in English. The past of eat as ate instead of *eated; the plural of child as children; the spelling of knight and night. These aren't actually irregular — they are perfectly regular within the context of an older structural system. That structural system is no longer current, but certain common elements of the language have become fixed with their older forms.
All language is systematic. Even something as crazy as the conjugation of the verb to be in English can be explained in terms of historical development. Our modern verb to be (and its forms am, are, was, were) is actually a few different verbs of being combined into one. Looking at Old English, these different verbs existed simultaneously, so one finds examples of the verb beon and the verb wesan. Over time, the language simplified into one verbal... mess, really. But the verb to be is so common that it can stay completely irregular.
The same principles hold true for all languages. Irregularities can always be explained, and usually by an examination of the history and development of the language. English is an extreme case because of its extensive contact with other languages. It's a hybrid, made up of Old English, Old Norse, Latin, French, and a smattering of other languages. Taking some time to figure out what you're dealing with can save a lot of headaches when it comes to trying to figure out how things work and why they work the way they do.