The argument opens with a short story about a group of football fans and it is not until the end of the story that you realise that the fans in question are female. Because German requires the male form to be used even if there is a group of females and just one male, the argument for gender reform states that current practice perpetuates prejudiced thinking and always puts the female as secondary. Some areas already have rules in place to combat gender-discriminatory language. For example, job ads are not allowed to discriminate in terms of gender (which includes the language they use). And students at some universities are marked down if they fail to use inclusive language.
Solutions to this problem include simply listing both male and female versions whenever referring to a mixed gender group. For example, instead of addressing just "Studenten" (male students), you would have to address both Studenten and Studentinnen (female students). Another solution is to use participles, which are gender neutral. In this example, you would say "Studierende" (people who study). Some argue that the male and female genders should be got rid of completely, using the neutral form to refer to all genders. Others believe that soon the female form will take over, as this it is what the majority of German learners fall back to when in doubt.
The counter-argument states that gender-neutral language is simply too complicated and long-winded. It also argues that everybody knows that the use of the male form includes females anyway. Those against gender reform claim that it will create a world of unreadable and unlistenable language. The article in Die Zeit gives an example of one change that would be needed for gender-neutral langauge: the disclaimer cited at the end of all German adverts for medicines would become much longer, recommending viewers to speak their male doctor or female doctor and male pharmacist or female pharmacist!
Luckily, English is largely safe from this minefield. In many cases, texts that would have used "he/his/him" in the past are now moving towards the plural form. One other bonus is that English is much more likely to address the reader or viewer as "you", meaning we don't have to worry about anything beyond that.