We should try to keep each point as short as possible. These arguments should be a resource for people who want to approach a school, teacher, or related body to ask them to use Free Software.
Schools should teach children to be good members of the community, to help each other and to share with each other. With proprietary software, teachers are required to prevent such sharing and to tell the children that sharing of useful software is wrong. Using Free Software allows schools to set a better example and teach children to share and cooperate and thus join a whole community that shares knowledge.
Equality at home
With free software, teachers can give a copy to each student. Thus parents are not put in a position of making a financial decision, and children of families with less financial resources can learn with the same tools as every other child.
Learning to program
Some children will be interested in how software works, and some will be interested in writing software. When a school uses Free Software, they are in a position to help interested children learn about computers to any depth.
The possibility/freedom to tinker motivates children to learn more.
Learning to use software
Nowadays, it is not enough to know how to use a certain office program. Young employees need the capability to adapt to any software. It's important to understand the concepts underlying a whole category or type of software (such as a spreadsheet or a word-processor), not merely how to use a particular application. The variety of Free Software products teaches exactly this. For a better understanding, a comparison of different concepts and approaches (e.g. LyX/LaTeX vs. Open Office) is invaluable. Free Software permits students to learn how software works and thus how they can make the best use of it. A key skill, demanded by employers.
If children learn to do things a certain way in school, the easiest way for them to do that thing in their adult life is to continue to do it the same way. If schools teach children to rely on proprietary software, they are giving the child a dependency on something which they have to pay for and which generally discourages sharing and good will in society. However, if a school teaches children to rely on Free Software, the software can never be taken away from the child (even in the child's adult life) and the child can continue using this software while helping others by sharing it.
Using and teaching Free Software also makes the school itself independent from any commercial interests.
No trouble with licenses
With Free Software, there are no worries about expiry dates or costs of the licenses. Free Software stays free in every sense. There is no risk to mislead any child to use an illegal copy (see also: "Equality at home").
Easy to administer
There are several ready-to-use solutions for many use-cases in educational scenarios. Maintenance of Free Software systems is highly automated and hence timesaving. Security and other updates can be implemented in a minute.
Free Software is stable, secure and reliable.
No licence fees
Free Software can save the school money. Since there are no license charges, the money can be use to train the teachers or for technical support to disburden the teachers.
Better use of old hardware
Free Software can be used with minimal hardware requirements on almost any hardware. Thus, it saves money again.
Modifiable, learning in native language
Free Software applications are being translated into almost any language (even into those where a translation could not be afforded by a proprietary software developer). Thus each child can learn and focus on the actual subject without any language barriers. It can even be adopted to local cultural characteristics
Sources for further information
http://www.salzburg.luga.or.at/linux_in_der_schule.html Argumentation pro Free Software in German (GFDL)